Two-dimensional confinement of heavy fermions

International Nuclear Information System (INIS)

Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito

2010-01-01

Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)

Fermion tunneling from higher-dimensional black holes

International Nuclear Information System (INIS)

Lin Kai; Yang Shuzheng

2009-01-01

Via the semiclassical approximation method, we study the 1/2-spin fermion tunneling from a higher-dimensional black hole. In our work, the Dirac equations are transformed into a simple form, and then we simplify the fermion tunneling research to the study of the Hamilton-Jacobi equation in curved space-time. Finally, we get the fermion tunneling rates and the Hawking temperatures at the event horizon of higher-dimensional black holes. We study fermion tunneling of a higher-dimensional Schwarzschild black hole and a higher-dimensional spherically symmetric quintessence black hole. In fact, this method is also applicable to the study of fermion tunneling from four-dimensional or lower-dimensional black holes, and we will take the rainbow-Finsler black hole as an example in order to make the fact explicit.

Compatible orders and fermion-induced emergent symmetry in Dirac systems

Science.gov (United States)

Janssen, Lukas; Herbut, Igor F.; Scherer, Michael M.

2018-01-01

We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with O (N1) and O (N2) symmetries, respectively. Using ɛ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent O (N1+N2) symmetry for arbitrary values of N1 and N2 and fermion flavor numbers Nf as long as the corresponding representation of the Clifford algebra exists. Small O (N ) -breaking perturbations near the chiral O (N ) fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic O (N ) fixed point, which is stable only when N by-product, we obtain predictions for the critical behavior of the chiral O (N ) universality classes for arbitrary N and fermion flavor number Nf. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.

Relativistic space-charge-limited current for massive Dirac fermions

Science.gov (United States)

Ang, Y. S.; Zubair, M.; Ang, L. K.

2017-04-01

A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, J ∝Vα/Lβ , for a finite band-gap Dirac material of length L biased under a voltage V . In one-dimensional (1D) bulk geometry, our model allows (α ,β ) to vary from (2,3) for the nonrelativistic model in traditional solids to (3/2,2) for the ultrarelativistic model of massless Dirac fermions. For 2D thin-film geometry we obtain α =β , which varies between 2 and 3/2, respectively, at the nonrelativistic and ultrarelativistic limits. We further provide rigorous proof based on a Green's-function approach that for a uniform SCLC model described by carrier-density-dependent mobility, the scaling relations of the 1D bulk model can be directly mapped into the case of 2D thin film for any contact geometries. Our simplified approach provides a convenient tool to obtain the 2D thin-film SCLC scaling relations without the need of explicitly solving the complicated 2D problems. Finally, this work clarifies the inconsistency in using the traditional SCLC models to explain the experimental measurement of a 2D Dirac semiconductor. We conclude that the voltage scaling 3 /2 <α <2 is a distinct signature of massive Dirac fermions in a Dirac semiconductor and is in agreement with experimental SCLC measurements in MoS2.

Massive chiral fermions: a natural account of chiral phenomenology in the framework of Dirac's fermion theory

International Nuclear Information System (INIS)

Ziino, G.

1989-01-01

We assume a strictly invariant definition of the Dirac parity operator under fermion ↔ antifermion exchange. We see that the opposite-intrinsic-parity condition then requires two opposite-mass Dirac equations for the fermion and the antifermion. This leads us to introduce an asymptotically left-handed (fermion) and right-handed (antifermion) chiral field, as just an alternative basis in the internal space spanned by the new pair of charge-conjugate Dirac fields. Hence a dual intrinsic model of a spin - 1/2 massive fermion is drawn: it predicts the coexistence of two anticommuting general varieties of conserved charges, namely a scalar variety, responsible for parity-invariant phenomenology, plus a pseudoscalar one, responsible for chiral phenomenology. In this light, CP-symmetry is seen to be nothing but P-symmetry; and a spontaneous CP-violation mechanism is also derived, that should work in any single process occurring via both scalar-and pseudoscalar-charge interactions. We show, at last, that our scheme automatically yields Weyl's one for a merely left-handed neutrino and a merely right-handed antineutrino, further assigning them the special meaning of pure pseudoscalar-charge objects. Some general consequences as regards magnetic monopoles are briefly discussed too

Chiral anomaly, fermionic determinant and two dimensional models

International Nuclear Information System (INIS)

Rego Monteiro, M.A. do.

1985-01-01

The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt

On the confinement of a Dirac particle to a two-dimensional ring

International Nuclear Information System (INIS)

Bakke, K.; Furtado, C.

2012-01-01

In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring for systems described by the Dirac equation by introducing a new coupling into the Dirac equation. We show that the introduction of this new coupling into the Dirac equation yields a generalization of the two-dimensional quantum ring model proposed by Tan and Inkson [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635] for relativistic spin-half quantum particles. -- Highlights: ► Two-dimensional ring model for condensed matter systems described by the Dirac equation. ► Exact solutions of the Dirac equation. ► Persistent currents for Dirac-like systems confined to a two-dimensional quantum ring.

Magnetotransport in Layered Dirac Fermion System Coupled with Magnetic Moments

Science.gov (United States)

Iwasaki, Yoshiki; Morinari, Takao

2018-03-01

We theoretically investigate the magnetotransport of Dirac fermions coupled with localized moments to understand the physical properties of the Dirac material EuMnBi2. Using an interlayer hopping form, which simplifies the complicated interaction between the layers of Dirac fermions and the layers of magnetic moments in EuMnBi2, the theory reproduces most of the features observed in this system. The hysteresis observed in EuMnBi2 can be caused by the valley splitting that is induced by the spin-orbit coupling and the external magnetic field with the molecular field created by localized moments. Our theory suggests that the magnetotransport in EuMnBi2 is due to the interplay among Dirac fermions, localized moments, and spin-orbit coupling.

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd₃As₂.

Science.gov (United States)

Jeon, Sangjun; Zhou, Brian B; Gyenis, Andras; Feldman, Benjamin E; Kimchi, Itamar; Potter, Andrew C; Gibson, Quinn D; Cava, Robert J; Vishwanath, Ashvin; Yazdani, Ali

2014-09-01

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

Two-dimensional thermofield bosonization

International Nuclear Information System (INIS)

Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

2005-01-01

The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized

Fermion-induced quantum critical points.

Science.gov (United States)

Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

2017-08-22

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

Few layer epitaxial germanene: a novel two-dimensional Dirac material

OpenAIRE

María Eugenia Dávila; Guy Le Lay

2016-01-01

Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established o...

Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly

International Nuclear Information System (INIS)

Yoshioka, Nobuyuki; Matsuura, Hiroyasu; Ogata, Masao

2016-01-01

We propose a new physical interpretation of the Diophantine equation of σ xy for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called 'subcells', which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of σ xy , that are consistent with the Diophantine equation: Landau quantization of (1) massless Dirac fermions or (2) free fermions in Hofstadter's butterfly. (author)

Axial anomaly and index theorem for Dirac-Kaehler fermions

International Nuclear Information System (INIS)

Fonseca Junior, C.A.L. da.

1985-02-01

Some aspects of topological influence on gauge field theory are analysed, considering the geometry and differential topology methods. A review of concepts of differential forms, fibered spaces, connection and curvature, showing an interpretation of gauge theory in this context, is presented. The question of fermions, analysing in details the Dirac-Kaehler which fermionic particle is considered a general differential form, is studied. It is shown how the explicit expressions in function of the Dirac spinor components vary with the Dirac matrix representation. The Dirac-Kahler equation contains 4 times (in 4 dimensions) the Dirac equation, each particle being associated an ideal at left of the algebra of general differential forms. These ideals and the SU(4) symmetry among them are also studied on the point of view of spinors and, the group of reduction to one of the ideals is identified as the Cartan subalgebra of this SU(4). Finally, the axial anomaly is calculated through the functional determinant given by the Dirac-Kaehler operator. The regularization method is the Seeley's coefficients. From that results a comparison of the index theorems for the twisted complexes of signature and spin, which proportionality is given by the number of the algebra ideals contained in the Dirac-Kaehler equation and which also manifests in the respective axial anomaly equations. (L.C.) [pt

Fermion unification model based on the intrinsic SU(8 symmetry of a generalized Dirac equation

Directory of Open Access Journals (Sweden)

Eckart eMarsch

2015-10-01

Full Text Available A natural generalization of the original Dirac spinor into a multi-component spinor is achieved, which corresponds to the single lepton and the three quarks of the first family of the standard model of elementary particle physics. Different fermions result from similarity transformations of the Dirac equation, but apparently there can be no more fermions according to the maximal multiplicity revealed in this study. Rotations in the fermion state space are achieved by the unitary generators of the U(1 and the SU(3 groups, corresponding to quantum electrodynamics (QED based on electric charge and chromodynamics (QCD based on colour charge. In addition to hypercharge the dual degree of freedom of hyperspin emerges, which occurs due to the duplicity implied by the two related (Weyl and Dirac representations of the Dirac equation. This yields the SU(2 symmetry of the weak interaction, which can be married to U(1 to generate the unified electroweak interaction as in the standard model. Therefore, the symmetry group encompassing all the three groups mentioned above is SU(8, which can accommodate and unify the observed eight basic stable fermions.

Interacting-fermion approximation in the two-dimensional ANNNI model

International Nuclear Information System (INIS)

Grynberg, M.D.; Ceva, H.

1990-12-01

We investigate the effect of including domain-walls interactions in the two-dimensional axial next-nearest-neighbor Ising or ANNNI model. At low temperatures this problem is reduced to a one-dimensional system of interacting fermions which can be treated exactly. It is found that the critical boundaries of the low-temperature phases are in good agreement with those obtained using a free-fermion approximation. In contrast with the monotonic behavior derived from the free-fermion approach, the wall density or wave number displays reentrant phenomena when the ratio of the next-nearest-neighbor and nearest-neighbor interactions is greater than one-half. (author). 17 refs, 2 figs

Magnetic susceptibility of Dirac fermions, Bi-Sb alloys, interacting Bloch fermions, dilute nonmagnetic alloys, and Kondo alloys

Energy Technology Data Exchange (ETDEWEB)

Buot, Felix A., E-mail: fbuot@gmu.edu [Computational Materials Science Center, George Mason University, Fairfax, VA 22030 (United States); TCSE Center, Spintronics Group, Physics Department, University of San Carlos, Talamban, Cebu 6000 (Philippines); C& LB Research Institute, Carmen, Cebu 6005 (Philippines); Otadoy, Roland E.S.; Rivero, Karla B. [TCSE Center, Spintronics Group, Physics Department, University of San Carlos, Talamban, Cebu 6000 (Philippines)

2017-03-01

Wide ranging interest in Dirac Hamiltonian is due to the emergence of novel materials, namely, graphene, topological insulators and superconductors, the newly-discovered Weyl semimetals, and still actively-sought after Majorana fermions in real materials. We give a brief review of the relativistic Dirac quantum mechanics and its impact in the developments of modern physics. The quantum band dynamics of Dirac Hamiltonian is crucial in resolving the giant diamagnetism of bismuth and Bi-Sb alloys. Quantitative agreement of the theory with the experiments on Bi-Sb alloys has been achieved, and physically meaningful contributions to the diamagnetism has been identified. We also treat relativistic Dirac fermion as an interband dynamics in uniform magnetic fields. For the interacting Bloch electrons, the role of translation symmetry for calculating the magnetic susceptibility avoids any approximation to second order in the field. The expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results. The unified treatment of all the above calculations is based on the lattice Weyl-Wigner formulation of discrete phase-space quantum mechanics. For completeness, the magnetic susceptibility of Kondo alloys is also given since Dirac fermions in conduction band and magnetic impurities exhibit Kondo effect.

Fermionic quasinormal modes for two-dimensional Horava-Lifshitz black holes

Energy Technology Data Exchange (ETDEWEB)

Stetsko, M.M. [Ivan Franko National University of Lviv, Department for Theoretical Physics, Lviv (Ukraine)

2017-06-15

To obtain fermionic quasinormal modes, the Dirac equation for two types of black holes is investigated. It is shown that two different geometries lead to distinctive types of quasinormal modes, while the boundary conditions imposed on the solutions in both cases are identical. For the first type of black hole, the quasinormal modes have continuous spectrum with negative imaginary part that provides the stability of perturbations. For the second type of the black hole, the quasinormal modes have a discrete spectrum and are completely imaginary. (orig.)

Chirality correlation within Dirac eigenvectors from domain wall fermions

International Nuclear Information System (INIS)

Blum, T.; Christ, N.; Cristian, C.; Liao, X.; Liu, G.; Mawhinney, R.; Wu, L.; Zhestkov, Y.; Dawson, C.

2002-01-01

In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath et al. we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, β=6.0, larger lattices, 16 4 , and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitudes of the chirality density, |ψ † (x)γ 5 ψ(x)|, and the normal density, ψ † (x)ψ(x), for the low-lying Dirac eigenvectors

Dynamical class of a two-dimensional plasmonic Dirac system.

Science.gov (United States)

Silva, Érica de Mello

2015-10-01

A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.

Quantitative application of Fermi-Dirac functions of two- and three-dimensional systems

International Nuclear Information System (INIS)

Grimmer, D.P.; Luszczynski, K.; Salibi, N.

1981-01-01

Expressions for the various physical parameters of the ideal Fermi-Dirac gas in two dimensions are derived and compared to the corresponding three-dimensional expressions. These derivations show that the Fermi-Dirac functions most applicable to the two-dimensional problem are F/sub o/(eta), F 1 (eta), and F' 0 (eta). Analogous to the work of McDougall and Stoner in three dimensions, these functions and parameters derived from them are tabulated over the range of the argument, -4 3 He monolayer and bulk liquid 3 He nuclear magnetic susceptibilities, respectively, are considered. Calculational procedures of fitting data to theoretical parameters and criteria for judging the quality of fit of data to both two- and three-dimensional Fermi-Dirac values are discussed

Three Dimensional Dirac Semimetals

Science.gov (United States)

Zaheer, Saad

2014-03-01

Dirac points on the Fermi surface of two dimensional graphene are responsible for its unique electronic behavior. One can ask whether any three dimensional materials support similar pseudorelativistic physics in their bulk electronic spectra. This possibility has been investigated theoretically and is now supported by two successful experimental demonstrations reported during the last year. In this talk, I will summarize the various ways in which Dirac semimetals can be realized in three dimensions with primary focus on a specific theory developed on the basis of representations of crystal spacegroups. A three dimensional Dirac (Weyl) semimetal can appear in the presence (absence) of inversion symmetry by tuning parameters to the phase boundary separating a bulk insulating and a topological insulating phase. More generally, we find that specific rules governing crystal symmetry representations of electrons with spin lead to robust Dirac points at high symmetry points in the Brillouin zone. Combining these rules with microscopic considerations identifies six candidate Dirac semimetals. Another method towards engineering Dirac semimetals involves combining crystal symmetry and band inversion. Several candidate materials have been proposed utilizing this mechanism and one of the candidates has been successfully demonstrated as a Dirac semimetal in two independent experiments. Work carried out in collaboration with: Julia A. Steinberg, Steve M. Young, J.C.Y. Teo, C.L. Kane, E.J. Mele and Andrew M. Rappe.

Axial anomaly and index theorem for Dirac-Kaehler fermions

International Nuclear Information System (INIS)

Linhares, C.A.; Mignaco, J.A.; Monteiro, M.A.R.

1985-01-01

We present the calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2 n/2 (n:number of dimensions) and agrees with the expressions from the index theorem. (author) [pt

Axial anomaly and index theorem for Dirac-Kaehler fermions

International Nuclear Information System (INIS)

Linhares, C.A.; Mignaco, J.A.; Rego Monteiro, M.A.

1985-01-01

We present a calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2sup(π/2) (n: number of dimensions) and agrees with the expressions from the index theorem. (orig.)

Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator

Science.gov (United States)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2017-12-01

The Atiyah-Patodi-Singer (APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a nonlocal boundary condition known as the "APS boundary condition" by hand, which is unlikely to be realized in the materials. In this work, we attempt to reformulate the APS index in a "physicist-friendly" way for a simple setup with U (1 ) or S U (N ) gauge group on a flat four-dimensional Euclidean space. We find that the same index as APS is obtained from the domain-wall fermion Dirac operator with a local boundary condition, which is naturally given by the kink structure in the mass term. As the boundary condition does not depend on the gauge fields, our new definition of the index is easy to compute with the standard Fujikawa method.

Dirac cones beyond the honeycomb lattice : a symmetry based approach

NARCIS (Netherlands)

Miert, G. van; de Morais Smith, Cristiane

2016-01-01

Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

Science.gov (United States)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

Qualitative analysis of trapped Dirac fermions in graphene

Czech Academy of Sciences Publication Activity Database

Jakubský, Vít; Krejčiřík, David

2014-01-01

Roč. 349, OCT (2014), s. 268-287 ISSN 0003-4916 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : graphene * Dirac fermion * confinement * Varitional principle Subject RIV: BE - Theoretical Physics Impact factor: 2.103, year: 2014

Fermionic greybody factors of two and five-dimensional dilatonic black holes

Energy Technology Data Exchange (ETDEWEB)

Becar, Ramon [Universidad Catolica de Temuco, Departamento de Ciencias Matematicas y Fisicas, Temuco (Chile); Gonzalez, P.A. [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica, Facultad de Ciencias, La Serena (Chile)

2014-08-15

We study fermionic perturbations in the background of a two and five-dimensional dilatonic black holes. Then, we compute the reflection and transmission coefficients and the absorption cross section for fermionic fields, and we show numerically that the absorption cross section vanishes in the low and high frequency limit. Also we find that beyond a certain value of the horizon radius r{sub 0} the absorption cross section for five-dimensional dilatonic black hole is constant. Besides, we have find that the absorption cross section decreases for higher angular momentum, and it decreases when the mass of the fermionic field increases. (orig.)

The Dirac-Kaehler equation and fermions on the lattice

International Nuclear Information System (INIS)

Becher, P.

1982-05-01

The geometrical description of spinor fields by E. Kaehler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice. (orig.)

Considerations concering the generalization of the Dirac equations to unstable fermions

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Sirlin, Alberto

2014-08-01

We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-1/2 fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations and spinors, and explain the very simple relation that exists, in our formulation, between the unstable and stable cases. As an application of the generalized spinors, we evaluate the probability density. We also discuss the behavior of the generalized Dirac equations under time reversal.

Time-dependent massless Dirac fermions in graphene

Energy Technology Data Exchange (ETDEWEB)

Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)

2015-10-30

Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.

Landau quantization of Dirac fermions in graphene and its multilayers

Science.gov (United States)

Yin, Long-Jing; Bai, Ke-Ke; Wang, Wen-Xiao; Li, Si-Yu; Zhang, Yu; He, Lin

2017-08-01

When electrons are confined in a two-dimensional (2D) system, typical quantum-mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum-mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.

Surface states of a system of Dirac fermions: A minimal model

International Nuclear Information System (INIS)

Volkov, V. A.; Enaldiev, V. V.

2016-01-01

A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and nontopological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed.

Surface states of a system of Dirac fermions: A minimal model

Energy Technology Data Exchange (ETDEWEB)

Volkov, V. A., E-mail: volkov.v.a@gmail.com; Enaldiev, V. V. [Russian Academy of Sciences, Kotel’nikov Institute of Radio Engineering and Electronics (Russian Federation)

2016-03-15

A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and nontopological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed.

Thermoelectric Transport Signatures of Dirac Composite Fermions in the Half-Filled Landau Level

Science.gov (United States)

Potter, Andrew C.; Serbyn, Maksym; Vishwanath, Ashvin

2016-07-01

The half-filled Landau level is expected to be approximately particle-hole symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of the compressible state observed at this filling. Recent work indicates that, when particle-hole symmetry is preserved, the composite fermions experience a quantized π -Berry phase upon winding around the composite Fermi surface, analogous to Dirac fermions at the surface of a 3D topological insulator. In contrast, the effective low-energy theory of the composite fermion liquid originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry phase. In this paper, we explain how thermoelectric transport measurements can be used to test the Dirac nature of the composite fermions by quantitatively extracting this Berry phase. First, we point out that longitudinal thermopower (Seebeck effect) is nonvanishing because of the unusual nature of particle-hole symmetry in this context and is not sensitive to the Berry phase. In contrast, we find that off-diagonal thermopower (Nernst effect) is directly related to the topological structure of the composite Fermi surface, vanishing for zero Berry phase and taking its maximal value for π Berry phase. In contrast, in purely electrical transport signatures, the Berry phase contributions appear as small corrections to a large background signal, making the Nernst effect a promising diagnostic of the Dirac nature of composite fermions.

Micromagnetic sensors and Dirac fermions in HgTe heterostructures

International Nuclear Information System (INIS)

Buettner, Bastian

2012-01-01

Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ''Experimentelle Physik'' of the University of Wuerzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te-heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-μm magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T=4.2 K for a (200.200) nm 2 Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely δB∼100 μT, the nanoscale sensor size yields an outstanding flux resolution of δΦ=2.10 -3 Φ 0 , where Φ 0 =h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as δM∼10 2 μ B , with the magnetic moment of a single electron μ B , the Bohr magneton. The further examination of a permalloy nanomagnet with a cross-section of (100.20) nm 2 confirms the expected resolution ability

Dirac matter

CERN Document Server

Rivasseau, Vincent; Fuchs, Jean-Nöel

2017-01-01

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other mater...

A semi-classical analysis of Dirac fermions in 2+1 dimensions

International Nuclear Information System (INIS)

Maiti, Moitri; Shankar, R

2012-01-01

We investigate the semi-classical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the α matrices by two generators of the SU(2) group in the (2S + 1)-dimensional representation and doing a certain scaling, we formulate an S → ∞ limit where the orbital and the spinor degrees become classical. We solve for the classical trajectories for a free particle on a cylinder and a particle in a constant magnetic field. We compare the semi-classical spectrum, obtained by Bohr–Sommerfeld quantization with the exact quantum spectrum for low values of S. For the free particle, the semi-classical spectrum is exact. For the particle in a constant magnetic field, the semi-classical spectrum reproduces all the qualitative features of the exact quantum spectrum at all S. The quantitative fit for S = 1/2 is reasonably good. (paper)

Fermions Tunneling from Higher-Dimensional Reissner-Nordström Black Hole: Semiclassical and Beyond Semiclassical Approximation

Directory of Open Access Journals (Sweden)

ShuZheng Yang

2016-01-01

Full Text Available Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordström black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordström black hole space-time. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.

Dirac materials

OpenAIRE

Wehling, T. O.; Black-Schaffer, A. M.; Balatsky, A. V.

2014-01-01

A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials''. In order to establish this class of materials, we illustrate how Dirac fermions ...

Multigrid for Staggered Lattice Fermions

Energy Technology Data Exchange (ETDEWEB)

Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.

2018-01-23

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

Fermion emission in a two-dimensional black hole space-time

International Nuclear Information System (INIS)

Wanders, G.

1994-01-01

We investigate massless fermion production by a two-dimensional dilatonic black hole. Our analysis is based on the Bogoliubov transformation relating the outgoing fermion field observed outside the black hole horizon to the incoming field present before the black hole creation. It takes full account of the fact that the transformation is neither invertible nor unitarily implementable. The particle content of the outgoing radiation is specified by means of inclusive probabilities for the detection of sets of outgoing fermions and antifermions in given states. For states localized near the horizon these probabilities characterize a thermal equilibrium state. The way the probabilities become thermal as one approaches the horizon is discussed in detail

Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals

KAUST Repository

Li, Yan

2013-01-01

We developed a selection rule for Dirac-like points in two-dimensional dielectric photonic crystals. The rule is derived from a perturbation theory and states that a non-zero, mode-coupling integral between the degenerate Bloch states guarantees a Dirac-like point, regardless of the type of the degeneracy. In fact, the selection rule can also be determined from the symmetry of the Bloch states even without computing the integral. Thus, the existence of Dirac-like points can be quickly and conclusively predicted for various photonic crystals independent of wave polarization, lattice structure, and composition. © 2013 Optical Society of America.

Fermions as generalized Ising models

Directory of Open Access Journals (Sweden)

C. Wetterich

2017-04-01

Full Text Available We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.

Dirac particle tunneling from black rings

International Nuclear Information System (INIS)

Jiang Qingquan

2008-01-01

Recent research shows that Hawking radiation can be treated as a quantum tunneling process, and Hawking temperatures of Dirac particles across the horizon of a black hole can be correctly recovered via the fermion tunneling method. In this paper, motivated by the fermion tunneling method, we attempt to apply the analysis to derive Hawking radiation of Dirac particles via tunneling from black ring solutions of 5-dimensional Einstein-Maxwell-dilaton gravity theory. Finally, it is interesting to find that, as in the black hole case, fermion tunneling can also result in correct Hawking temperatures for the rotating neutral, dipole, and charged black rings.

Absence of vortex condensation in a two dimensional fermionic XY model

International Nuclear Information System (INIS)

Cecile, D. J.; Chandrasekharan, Shailesh

2008-01-01

Motivated by a puzzle in the study of two-dimensional lattice quantum electrodynamics with staggered fermions, we construct a two-dimensional fermionic model with a global U(1) symmetry. Our model can be mapped into a model of closed packed dimers and plaquettes. Although the model has the same symmetries as the XY model, we show numerically that the model lacks the well-known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing the absence of a phase with vortex condensation. In other words the low energy physics is described by a noncompact U(1) field theory. We show that by introducing an even number of layers one can introduce vortex condensation within the model and thus also induce a Kosterlitz-Thouless transition.

Electrodynamic properties of the semimetallic Dirac material SrMnB i2 : Two-carrier-model analysis

Science.gov (United States)

Park, H. J.; Park, Byung Cheol; Lee, Min-Cheol; Jeong, D. W.; Park, Joonbum; Kim, Jun Sung; Ji, Hyo Seok; Shim, J. H.; Kim, K. W.; Moon, S. J.; Kim, Hyeong-Do; Cho, Deok-Yong; Noh, T. W.

2017-10-01

The electrodynamics of free carriers in the semimetallic Dirac material SrMnB i2 was investigated using optical spectroscopy and first-principles calculations. Using a two-carrier-model analysis, the total free-carrier response was successfully decomposed into individual contributions from Dirac fermions and non-Dirac free carriers. Possible roles of chiral pseudospin, spin-orbit interaction (SOI), antiferromagnetism, and electron-phonon (e -p h ) coupling in the Dirac fermion transport were also addressed. The Dirac fermions possess a low scattering rate of ˜10 meV at low temperature and thereby experience coherent transport. However, at high temperatures, we observed that the Dirac fermion transport becomes significantly incoherent, possibly due to strong e -p h interactions. The SOI-induced gap and antiferromagnetism play minor roles in the electrodynamics of the free carriers in SrMnB i2 . We also observed a seemingly optical-gap-like feature near 120 meV, which emerges at low temperatures but becomes filled in with increasing temperature. This gap-filling phenomenon is ascribed to phonon-assisted indirect transitions promoted at high temperatures.

Micromagnetic sensors and Dirac fermions in HgTe heterostructures

Energy Technology Data Exchange (ETDEWEB)

Buettner, Bastian

2012-08-06

Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ''Experimentelle Physik'' of the University of Wuerzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te-heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-{mu}m magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T=4.2 K for a (200.200) nm{sup 2} Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely {delta}B{approx}100 {mu}T, the nanoscale sensor size yields an outstanding flux resolution of {delta}{Phi}=2.10{sup -3} {Phi}{sub 0}, where {Phi}{sub 0}=h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as {delta}M{approx}10{sup 2} {mu}{sub B}, with the magnetic moment of a single electron {mu}{sub B}, the Bohr magneton. The further examination of a permalloy nanomagnet with a

Micromagnetic sensors and Dirac fermions in HgTe heterostructures

Energy Technology Data Exchange (ETDEWEB)

Buettner, Bastian

2012-08-06

Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ''Experimentelle Physik'' of the University of Wuerzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te-heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-{mu}m magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T=4.2 K for a (200.200) nm{sup 2} Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely {delta}B{approx}100 {mu}T, the nanoscale sensor size yields an outstanding flux resolution of {delta}{Phi}=2.10{sup -3} {Phi}{sub 0}, where {Phi}{sub 0}=h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as {delta}M{approx}10{sup 2} {mu}{sub B}, with the magnetic moment of a single electron {mu}{sub B}, the Bohr magneton. The further examination of a permalloy

Infrared magneto-spectroscopy of two-dimensional and three-dimensional massless fermions: A comparison

Energy Technology Data Exchange (ETDEWEB)

Orlita, M., E-mail: milan.orlita@lncmi.cnrs.fr [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2 (Czech Republic); Faugeras, C.; Barra, A.-L.; Martinez, G.; Potemski, M. [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Basko, D. M. [LPMMC UMR 5493, Université Grenoble 1/CNRS, B.P. 166, 38042 Grenoble (France); Zholudev, M. S. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Teppe, F.; Knap, W. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Gavrilenko, V. I. [Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Mikhailov, N. N.; Dvoretskii, S. A. [A.V. Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090 (Russian Federation); Neugebauer, P. [Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, C. [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Institut Néel/CNRS-UJF BP 166, F-38042 Grenoble Cedex 9 (France); Heer, W. A. de [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

2015-03-21

Here, we report on a magneto-optical study of two distinct systems hosting massless fermions—two-dimensional graphene and three-dimensional HgCdTe tuned to the zero band gap condition at the point of the semiconductor-to-semimetal topological transition. Both materials exhibit, in the quantum regime, a fairly rich magneto-optical response, which is composed from a series of intra- and interband inter-Landau level resonances with for massless fermions typical √(B) dependence. The impact of the system's dimensionality and of the strength of the spin-orbit interaction on the optical response is also discussed.

6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum

Directory of Open Access Journals (Sweden)

Yukihiro Fujimoto

2017-09-01

Full Text Available We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i 4d-chirality positive components being zero at the boundaries and (ii internal chirality positive components being zero at the boundaries. In the case of (i, twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter θ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value, θ contributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameter θ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii, this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.

Identifying Dirac cones in carbon allotropes with square symmetry

Energy Technology Data Exchange (ETDEWEB)

Wang, Jinying [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Huang, Huaqing; Duan, Wenhui [Department of Physics, Tsinghua University, Beijing 100084 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); State Key Laboratory for Structural Chemistry of Unstable and Stable Species and Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)

2013-11-14

A theoretical study is conducted to search for Dirac cones in two-dimensional carbon allotropes with square symmetry. By enumerating the carbon atoms in a unit cell up to 12, an allotrope with octatomic rings is recognized to possess Dirac cones under a simple tight-binding approach. The obtained Dirac cones are accompanied by flat bands at the Fermi level, and the resulting massless Dirac-Weyl fermions are chiral particles with a pseudospin of S = 1, rather than the conventional S = 1/2 of graphene. The spin-1 Dirac cones are also predicted to exist in hexagonal graphene antidot lattices.

Harmonically trapped dipolar fermions in a two-dimensional square lattice

DEFF Research Database (Denmark)

Larsen, Anne-Louise G.; Bruun, Georg

2012-01-01

We consider dipolar fermions in a two-dimensional square lattice and a harmonic trapping potential. The anisotropy of the dipolar interaction combined with the lattice leads to transitions between phases with density order of different symmetries. We show that the attractive part of the dipolar...

Spin texture of the surface state of three-dimensional Dirac material Ca3PbO

Science.gov (United States)

Kariyado, Toshikaze

2015-04-01

The bulk and surface electronic structures of a candidate three-dimensional Dirac material Ca3PbO and its family are discussed especially focusing on the spin texture on the surface states. We first explain the basic features of the bulk band structure of Ca3PbO, such as emergence of Dirac fermions near the Fermi energy, and compare it with the other known three-dimensional Dirac semimetals. Then, the surface bands and spin-texture on them are investigated in detail. It is shown that the surface bands exhibit strong momentum-spin locking, which may be useful in some application for spin manipulation, induced by a combination of the inversion symmetry breaking at the surface and the strong spin-orbit coupling of Pb atoms. The surface band structure and the spin-textures are sensitive to the surface types.

Spin texture of the surface state of three-dimensional Dirac material Ca3PbO

International Nuclear Information System (INIS)

Kariyado, Toshikaze

2015-01-01

The bulk and surface electronic structures of a candidate three-dimensional Dirac material Ca 3 PbO and its family are discussed especially focusing on the spin texture on the surface states. We first explain the basic features of the bulk band structure of Ca 3 PbO, such as emergence of Dirac fermions near the Fermi energy, and compare it with the other known three-dimensional Dirac semimetals. Then, the surface bands and spin-texture on them are investigated in detail. It is shown that the surface bands exhibit strong momentum-spin locking, which may be useful in some application for spin manipulation, induced by a combination of the inversion symmetry breaking at the surface and the strong spin-orbit coupling of Pb atoms. The surface band structure and the spin-textures are sensitive to the surface types. (paper)

Charged Fermions Tunneling from a Rotating Charged Black Hole in 5-Dimensional Gauged Supergravity

International Nuclear Information System (INIS)

Li Huiling; Lin Rong; Wang Chuanyin

2010-01-01

Recent research shows that Hawking radiation from black hole horizon can be treated as a quantum tunneling process, and fermions tunneling method can successfully recover Hawking temperature. In this tunneling framework, choosing a set of appropriate matrices γ μ is an important technique for fermions tunneling method. In this paper, motivated by Kerner and Man's fermions tunneling method of 4 dimension black holes, we further improve the analysis to investigate Hawking tunneling radiation from a rotating charged black hole in 5-dimensional gauged supergravity by constructing a set of appropriate matrices γ μ for general covariant Dirac equation. Finally, the expected Hawking temperature of the black hole is correctly recovered, which takes the same form as that obtained by other methods. This method is universal, and can also be directly extend to the other different-type 5-dimensional charged black holes.

Dirac-Kahler fermion with noncommutative differential forms on a lattice

International Nuclear Information System (INIS)

Kanamori, I.; Kawamoto, N.

2004-01-01

Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-Kaehler fermion on the lattice

Dirac fermions in nontrivial topology black hole backgrounds

International Nuclear Information System (INIS)

Gozdz, Marek; Nakonieczny, Lukasz; Rogatko, Marek

2010-01-01

We discuss the behavior of the Dirac fermions in a general spherically symmetric black hole background with a nontrivial topology of the event horizon. Both massive and massless cases are taken into account. We will conduct an analytical study of intermediate and late-time behavior of massive Dirac hair in the background of a black hole with a global monopole and dilaton black hole pierced by a cosmic string. In the case of a global monopole swallowed by a static black hole, the intermediate late-time behavior depends on the mass of the Dirac field, the multiple number of the wave mode, and the global monopole parameter. The late-time behavior is quite independent of these factors and has a decay rate proportional to t -5/6 . As far as the black hole pierced by a cosmic string is concerned, the intermediate late-time behavior depends only on the hair mass and the multipole number of the wave mode, while the late-time behavior dependence is the same as in the previous case. The main modification stems from the topology of the S 2 sphere pierced by a cosmic string. This factor modifies the eigenvalues of the Dirac operator acting on the transverse manifold.

Chiral Tricritical Point: A New Universality Class in Dirac Systems

Science.gov (United States)

Yin, Shuai; Jian, Shao-Kai; Yao, Hong

2018-05-01

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

Science.gov (United States)

Zhu, Yan-Qing; Zhang, Dan-Wei; Yan, Hui; Xing, Ding-Yu; Zhu, Shi-Liang

2017-09-01

The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct two- and three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named as Maxwell fermions. We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions, Maxwell points may have nontrivial monopole charges of ±2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

Electric-dipole-induced universality for Dirac fermions in graphene.

Science.gov (United States)

De Martino, Alessandro; Klöpfer, Denis; Matrasulov, Davron; Egger, Reinhold

2014-05-09

We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accommodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.

Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

Science.gov (United States)

Banerjee, S.; Fransson, J.; Black-Schaffer, A. M.; Ågren, H.; Balatsky, A. V.

2016-04-01

We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.

Twisting dirac fermions: circular dichroism in bilayer graphene

Science.gov (United States)

Suárez Morell, E.; Chico, Leonor; Brey, Luis

2017-09-01

Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions’ helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers.

Pythagoras's theorem on a two-dimensional lattice from a 'natural' Dirac operator and Connes's distance formula

Energy Technology Data Exchange (ETDEWEB)

Dai Jian [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: jdai@mail.phy.pku.edu.cn; Song Xingchang [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: songxc@ibm320h.phy.pku.edu.cn

2001-07-13

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as 'natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices. (author)

Probing Dirac fermion dynamics in topological insulator Bi2Se3 films with a scanning tunneling microscope.

Science.gov (United States)

Song, Can-Li; Wang, Lili; He, Ke; Ji, Shuai-Hua; Chen, Xi; Ma, Xu-Cun; Xue, Qi-Kun

2015-05-01

Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi2Se3 ultrathin films. At the two-dimensional limit, bulk electrons become quantized and the quantization can be controlled by the film thickness at a single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of the phase relaxation length lϕ and inelastic scattering lifetime τ of topological surface-state electrons. We find that τ exhibits a remarkable (E - EF)(-2) energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.

Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time

Energy Technology Data Exchange (ETDEWEB)

Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)

2014-11-15

This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)

Veselago focusing of anisotropic massless Dirac fermions

Science.gov (United States)

Zhang, Shu-Hui; Yang, Wen; Peeters, F. M.

2018-05-01

Massless Dirac fermions (MDFs) emerge as quasiparticles in various novel materials such as graphene and topological insulators, and they exhibit several intriguing properties, of which Veselago focusing is an outstanding example with a lot of possible applications. However, up to now Veselago focusing merely occurred in p-n junction devices based on the isotropic MDF, which lacks the tunability needed for realistic applications. Here, motivated by the emergence of novel Dirac materials, we investigate the propagation behaviors of anisotropic MDFs in such a p-n junction structure. By projecting the Hamiltonian of the anisotropic MDF to that of the isotropic MDF and deriving an exact analytical expression for the propagator, precise Veselago focusing is demonstrated without the need for mirror symmetry of the electron source and its focusing image. We show a tunable focusing position that can be used in a device to probe masked atom-scale defects. This study provides an innovative concept to realize Veselago focusing relevant for potential applications, and it paves the way for the design of novel electron optics devices by exploiting the anisotropic MDF.

Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

Science.gov (United States)

Nguyen, Dung Xuan; Gromov, Andrey; Son, Dam Thanh

2018-05-01

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

International Nuclear Information System (INIS)

Belvedere, L.V.; Souza Dutra, A. de; Natividade, C.P.; Queiroz, A.F. de

2002-01-01

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED 2 with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED 2 with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content

Hydrogenated borophene as a stable two-dimensional Dirac material with an ultrahigh Fermi velocity.

Science.gov (United States)

Xu, Li-Chun; Du, Aijun; Kou, Liangzhi

2016-10-05

The recent synthesis of monolayer borophene (triangular boron monolayer) on a substrate has opened the era of boron nanosheets (Science, 2015, 350, 1513), but the structural instability and a need to explore the novel physical properties are still open issues. Here we demonstrated that borophene can be stabilized by full surface hydrogenation (borophane), from first-principles calculations. Most interestingly, our calculations show that borophane has direction-dependent Dirac cones, which are mainly caused by the in-plane p x and p y orbitals of boron atoms. The Dirac fermions possess an ultrahigh Fermi velocity of up to 3.5 × 10 6 m s -1 under the HSE06 level, which is 4 times higher than that of graphene. The Young's moduli are calculated to be 190 and 120 GPa nm along two different directions, which are comparable to those of steel. The ultrahigh Fermi velocity and good mechanical features render borophane ideal for nanoelectronic applications.

Overview on the anomaly and Schwinger term in two dimensional QED

International Nuclear Information System (INIS)

Adam, C.; Bertlmann, R.A.; Hofer, P.

1993-01-01

The axial anomaly of two-dimensional QED is computed in different ways (perturbative, via dispersion integrals, path integral and index theorem) and their relation is discussed as well as the relation between anomaly, Schwinger term and the Dirac vacuum. Some features of the special case of massless fermions (Schwinger model) and some methods of exactly solving it are demonstrated. (authors)

Traditional Semiconductors in the Two-Dimensional Limit.

Science.gov (United States)

Lucking, Michael C; Xie, Weiyu; Choe, Duk-Hyun; West, Damien; Lu, Toh-Ming; Zhang, S B

2018-02-23

Interest in two-dimensional materials has exploded in recent years. Not only are they studied due to their novel electronic properties, such as the emergent Dirac fermion in graphene, but also as a new paradigm in which stacking layers of distinct two-dimensional materials may enable different functionality or devices. Here, through first-principles theory, we reveal a large new class of two-dimensional materials which are derived from traditional III-V, II-VI, and I-VII semiconductors. It is found that in the ultrathin limit the great majority of traditional binary semiconductors studied (a series of 28 semiconductors) are not only kinetically stable in a two-dimensional double layer honeycomb structure, but more energetically stable than the truncated wurtzite or zinc-blende structures associated with three dimensional bulk. These findings both greatly increase the landscape of two-dimensional materials and also demonstrate that in the double layer honeycomb form, even ordinary semiconductors, such as GaAs, can exhibit exotic topological properties.

Large linear magnetoresistance in a new Dirac material BaMnBi2

International Nuclear Information System (INIS)

Wang Yi-Yan; Yu Qiao-He; Xia Tian-Long

2016-01-01

Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles. Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials. In this paper, we report the synthesis of high quality single crystals of BaMnBi 2 and investigate the transport properties of the samples. BaMnBi 2 is a metal with an antiferromagnetic transition at T N = 288 K. The temperature dependence of magnetization displays different behavior from CaMnBi 2 and SrMnBi 2 , which suggests the possible different magnetic structure of BaMnBi 2 . The Hall data reveals electron-type carriers and a mobility μ (5 K) = 1500 cm 2 /V·s. Angle-dependent magnetoresistance reveals the quasi-two-dimensional (2D) Fermi surface in BaMnBi 2 . A crossover from semiclassical MR ∼ H 2 dependence in low field to MR ∼ H dependence in high field, which is attributed to the quantum limit of Dirac fermions, has been observed in magnetoresistance. Our results indicate the existence of Dirac fermions in BaMnBi 2 . (rapid communication)

Optical study of Dirac fermions and related phonon anomalies in the antiferromagnetic compound CaFeAsF

Science.gov (United States)

Xu, B.; Xiao, H.; Gao, B.; Ma, Y. H.; Mu, G.; Marsik, P.; Sheveleva, E.; Lyzwa, F.; Dai, Y. M.; Lobo, R. P. S. M.; Bernhard, C.

2018-05-01

We performed optical studies on CaFeAsF single crystals, a parent compound of the 1111-type iron-based superconductors that undergoes a structural phase transition from tetragonal to orthorhombic at Ts=121 K and a magnetic one to a spin density wave (SDW) state at TN=110 K. In the low-temperature optical conductivity spectrum, after the subtraction of a narrow Drude peak, we observe a pronounced singularity around 300 cm-1 that separates two regions of quasilinear conductivity. We outline that these characteristic absorption features are signatures of Dirac fermions, similar to what was previously reported for the BaFe2As2 system [Z.-G. Chen et al., Phys. Rev. Lett. 119, 096401 (2017), 10.1103/PhysRevLett.119.096401]. In support of this interpretation, we show that for the latter system this singular feature disappears rapidly upon electron and hole doping, as expected if it arises from a van Hove singularity in between two Dirac cones. Finally, we show that one of the infrared-active phonon modes (the Fe-As mode at 250 cm-1) develops a strongly asymmetric line shape in the SDW state and note that this behavior can be explained in terms of a strong coupling with the Dirac fermions.

Majorana and Majorana-Weyl fermions in lattice gauge theory

International Nuclear Information System (INIS)

Inagaki, Teruaki; Suzuki, Hiroshi

2004-01-01

In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factorized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find. (author)

Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field

Science.gov (United States)

Khalilov, V. R.

2017-12-01

Creation of charged fermion pair from a vacuum in so-called supercritical Coulomb potential is examined for the case when fermions can move only in the same (one) plane. In which case, quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with an usual (-a/r) Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states for such Hamiltonians in the corresponding Hilbert spaces of square-integrable functions. We determine the scattering amplitude in which the self-adjoint extension parameter is incorporated and then obtain equations implicitly defining possible discrete energy spectra of the self-adjoint Dirac Hamiltonians with a Coulomb potential. It is shown that this quantum system becomes unstable in the presence of a supercritical Coulomb potential which manifests in the appearance of quasi-stationary states in the lower (negative) energy continuum. The energy spectrum of those states is quasi-discrete, consists of broadened levels with widths related to the inverse lifetimes of the quasi-stationary states as well as the probability of creation of charged fermion pair by a supercritical Coulomb field. Explicit analytical expressions for the creation probabilities of charged (massive or massless) fermion pair are obtained in a supercritical Coulomb field.

Nonlinear and anisotropic polarization rotation in two-dimensional Dirac materials

Science.gov (United States)

Singh, Ashutosh; Ghosh, Saikat; Agarwal, Amit

2018-05-01

We predict nonlinear optical polarization rotation in two-dimensional massless Dirac systems including graphene and 8-P m m n borophene. When illuminated, a continuous-wave optical field leads to a nonlinear steady state of photoexcited carriers in the medium. The photoexcited population inversion and the interband coherence give rise to a finite transverse optical conductivity σx y(ω ) . This in turn leads to definitive signatures in associated Kerr and Faraday polarization rotation, which are measurable in a realistic experimental scenario.

Twelve inequivalent Dirac cones in two-dimensional ${\mathrm{ZrB}}_2$

Energy Technology Data Exchange (ETDEWEB)

Lopez-Bezanilla, Alejandro

2018-01-01

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB2 is presented. Two-dimensional ZrB2 is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is able to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. The versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.

Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling

DEFF Research Database (Denmark)

Marchukov, O. V.; Fedorov, D. V.; Jensen, A. S.

2015-01-01

We investigate a two-dimensional system of fermions with two internal (spin) degrees of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body short range repulsion. We obtain self-consistent mean-field $N...

Two-dimensional conductors with interactions and disorder from particle-vortex duality

Science.gov (United States)

Goldman, H.; Mulligan, M.; Raghu, S.; Torroba, G.; Zimet, M.

2017-12-01

We study Dirac fermions in two spatial dimensions (2D) coupled to strongly fluctuating U (1 ) gauge fields in the presence of quenched disorder. Such systems are dual to theories of free Dirac fermions, which are vortices of the original theory. In analogy to superconductivity, when these fermionic vortices localize, the original system becomes a perfect conductor, and when the vortices possess a finite conductivity, the original fermions do as well. We provide several realizations of this principle and thereby introduce examples of strongly interacting 2D metals that evade Anderson localization.

Magneto-transmission as a probe of Dirac fermions in bulk graphite

Czech Academy of Sciences Publication Activity Database

Orlita, Milan; Faugeras, C.; Martinez, G.; Maude, D. K.; Sadowski, M.L.; Schneider, J.M.; Potemski, M.

2008-01-01

Roč. 20, č. 45 (2008), 454223/1-454223/4 ISSN 0953-8984 R&D Projects: GA AV ČR KAN400100652 Grant - others:EC(XE) RITA -CT-2003-505474; ANR(FR) ANR-06-NANO-019 Institutional research plan: CEZ:AV0Z10100521 Keywords : bulk graphite * Dirac fermions * magnetic field Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.900, year: 2008

New one-flavor hybrid Monte Carlo simulation method for lattice fermions with γ5 hermiticity

International Nuclear Information System (INIS)

Ogawa, Kenji

2011-01-01

We propose a new method for Hybrid Monte Carlo (HMC) simulations with odd numbers of dynamical fermions on the lattice. It employs a different approach from polynomial or rational HMC. In this method, γ 5 hermiticity of the lattice Dirac operators is crucial and it can be applied to Wilson, domain-wall, and overlap fermions. We compare HMC simulations with two degenerate flavors and (1+1) degenerate flavors using optimal domain-wall fermions. The ratio of the efficiency, (number of accepted trajectories)/(simulation time), is about 3:2. The relation between pseudofermion action of chirally symmetric lattice fermions in four-dimensional (overlap) and five-dimensional (domain-wall) representation are also analyzed.

Chiral zero energy modes in two-dimensional disordered Dirac semimetals

Science.gov (United States)

Liu, Lei; Yu, Yan; Wu, Hai-Bin; Zhang, Yan-Yang; Liu, Jian-Jun; Li, Shu-Shen

2018-04-01

The vacancy-induced chiral zero energy modes (CZEMs) of chiral-unitary-class (AIII) and chiral-symplectic-class (CII) two-dimensional (2 D ) disordered Dirac semimetals realized on a square bipartite lattice are investigated numerically by using the Kubo-Greenwood formula with the kernel polynomial method. The results show that, for both systems, the CZEMs exhibit the critical delocalization. The CZEM conductivity remains a robust constant (i.e., σ CZEM≈1.05 e2/h ), which is insensitive to the sample sizes, the vacancy concentrations, and the numbers of moments of Chebyshev polynomials, i.e., the dephasing strength. For both kinds of chiral systems, the CZEM conductivities are almost identical. However, they are not equal to that of graphene (i.e., 4 e2/π h ), which belongs to the chiral orthogonal class (BDI) semimetal on a 2 D hexagonal bipartite lattice. In addition, for the case that the vacancy concentrations are different in the two sublattices, the CZEM conductivity vanishes, and thus both systems exhibit localization at the Dirac point. Moreover, a band gap and a mobility gap open around zero energy. The widths of the energy gaps and mobility gaps are increasing with larger vacancy concentration difference. The width of the mobility gap is greater than that of the band gap, and a δ -function-like peak of density of states emerges at the Dirac point within the band gap, implying the existence of numerous localized states.

Extra Z neutral bosons, families and heavy fermions

International Nuclear Information System (INIS)

Li Tiezhong

1989-08-01

The minimal Grand Unified Theories with three-family should include two extra Z neufral bosons which belong to the different broken scales. Georgi's argument on heavy Dirac fermions has been realized. These fermions should not be bizarre. The extra Z and Dirac fermions are not too heavy. The difficulty of the proton decay may be resolved

The first principle calculation of two-dimensional Dirac materials

Science.gov (United States)

Lu, Jin

2017-12-01

As the size of integrated device becoming increasingly small, from the last century, semiconductor industry is facing the enormous challenge to break the Moore’s law. The development of calculation, communication and automatic control have emergent expectation of new materials at the aspect of semiconductor industrial technology and science. In spite of silicon device, searching the alternative material with outstanding electronic properties has always been a research point. As the discovery of graphene, the research of two-dimensional Dirac material starts to express new vitality. This essay studied the development calculation of 2D material’s mobility and introduce some detailed information of some approximation method of the first principle calculation.

Competing effective interactions of Dirac electrons in the Spin–Fermion system

International Nuclear Information System (INIS)

Marino, E.C.; Nunes, Lizardo H.C.M.

2014-01-01

Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin–Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu–Jona-Lasinio-like, excitonic term and a spin–spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants. -- Highlights: •Antiferromagnetic Heisenberg–Kondo lattice model with itinerant Dirac fermions. •Integrating out the spins generates competing interactions: BCS-like, excitonic and magnetic. •Novel mechanism of superconductivity from magnetic interactions between the spins and electrons. •Dome-shaped dependence of the temperature on the chemical potential in agreement with pnictides

C4N3H monolayer: A two-dimensional organic Dirac material with high Fermi velocity

Science.gov (United States)

Pan, Hongzhe; Zhang, Hongyu; Sun, Yuanyuan; Li, Jianfu; Du, Youwei; Tang, Nujiang

2017-11-01

Searching for two-dimensional (2D) organic Dirac materials, which have more adaptable practical applications compared with inorganic ones, is of great significance and has been ongoing. However, only two such materials with low Fermi velocity have been discovered so far. Herein, we report the design of an organic monolayer with C4N3H stoichiometry that possesses fascinating structure and good stability in its free-standing state. More importantly, we demonstrate that this monolayer is a semimetal with anisotropic Dirac cones and very high Fermi velocity. This Fermi velocity is roughly one order of magnitude larger than the largest velocity ever reported in 2D organic Dirac materials, and it is comparable to that in graphene. The Dirac states in this monolayer arise from the extended π -electron conjugation system formed by the overlapping 2 pz orbitals of carbon and nitrogen atoms. Our finding paves the way to a search for more 2D organic Dirac materials with high Fermi velocity.

Bloch-Siegert shift in Dirac-Weyl fermionic systems

Science.gov (United States)

Kumar, Upendra; Kumar, Vipin; Enamullah, Setlur, Girish S.

2018-04-01

The Bloch-Siegert shift is a phenomenon in quantum optics, typically seen in two-level systems, when the driving field is sufficiently strong. The inclusion of frequency doubling effect (counter rotating term) in the conventional rotating wave approximation (RWA) changes the resonance condition thereby producing a rather small shift in the resonance condition, which is known as the Bloch-Siegert shift (BSS). Rabi oscillations in Dirac-Weyl fermionic systems exhibit anomalous behavior far from resonance, called anomalous Rabi oscillations. Therefore, in the present work, we study the phenomenon of the Bloch-Siegert shift in Weyl semimetal and topological insulator (TI) far from resonance, called anomalous Bloch-Siegert shift (ABSS). It is seen that the change in the resonance condition of anomalous Rabi oscillations is drastic in Weyl semimetal and TI. The ABSS in Weyl semimetals is highly anisotropic, whereas it is isotropic in TI. In case of TI, it is the Chern number which plays a crucial role to produce substantial change in the ABSS.

Fermion tunnels of higher-dimensional anti-de Sitter Schwarzschild black hole and its corrected entropy

Energy Technology Data Exchange (ETDEWEB)

Lin Kai, E-mail: lk314159@126.co [Institute of Theoretical Physics, China West Normal University, NanChong, SiChuan 637002 (China); Yang Shuzheng, E-mail: szyangcwnu@126.co [Institute of Theoretical Physics, China West Normal University, NanChong, SiChuan 637002 (China)

2009-10-12

Applying the method beyond semiclassical approximation, fermion tunneling from higher-dimensional anti-de Sitter Schwarzschild black hole is researched. In our work, the 'tortoise' coordinate transformation is introduced to simplify Dirac equation, so that the equation proves that only the (r-t) sector is important to our research. Because we only need to study the (r-t) sector, the Dirac equation is decomposed into several pairs of equations spontaneously, and we then prove the components of wave functions are proportional to each other in every pair of equations. Therefore, the suitable action forms of the wave functions are obtained, and finally the correctional Hawking temperature and entropy can be determined via the method beyond semiclassical approximation.

The Chiral Index of the Fermionic Signature Operator

OpenAIRE

Finster, Felix

2014-01-01

We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators thereon for which our index is non-trivial.

Lattice approximation of gauge theories with Dirac Kaehler fermions

International Nuclear Information System (INIS)

Joos, H.

1988-01-01

A program which tries to overcome the systematic difficulties caused by the lattice fermion problem by the consideration of models which describe Dirac fields by differential forms is reported. In the first lecture the formalism is developped and applied to the formulation of geometric QCD and of a Geometric Standard Model. The second lecture treats the characteristic symmetry problems which appear in the lattice approximation of geometric field theories. In the last lecture strong coupling dynamics of geometric QCD are considered with the final aim of a derivation of the quark model for the hadron spectrum. (author) [pt

Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS

OpenAIRE

Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R.

2016-01-01

Materials harboring exotic quasiparticles, such as Dirac and Weyl fermions\\cite{xu2015discovery,borisenko2015time,weng2015weyl,xu2015observation}, have garnered much attention from the physics and material science communities. These fermions are massless and, in some materials, have shown exceptional physical properties such as ultrahigh mobility and extremely large magnetoresistances \\cite{liang2015ultrahigh,ali2014large,du2015unsaturated,shekhar2015large}. Recently, new materials have been ...

Large linear magnetoresistance in a new Dirac material BaMnBi2

Science.gov (United States)

Wang, Yi-Yan; Yu, Qiao-He; Xia, Tian-Long

2016-10-01

Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles. Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials. In this paper, we report the synthesis of high quality single crystals of BaMnBi2 and investigate the transport properties of the samples. BaMnBi2 is a metal with an antiferromagnetic transition at T N = 288 K. The temperature dependence of magnetization displays different behavior from CaMnBi2 and SrMnBi2, which suggests the possible different magnetic structure of BaMnBi2. The Hall data reveals electron-type carriers and a mobility μ(5 K) = 1500 cm2/V·s. Angle-dependent magnetoresistance reveals the quasi-two-dimensional (2D) Fermi surface in BaMnBi2. A crossover from semiclassical MR ˜ H 2 dependence in low field to MR ˜ H dependence in high field, which is attributed to the quantum limit of Dirac fermions, has been observed in magnetoresistance. Our results indicate the existence of Dirac fermions in BaMnBi2. Project supported by the National Natural Science Foundation of China (Grant No. 11574391), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grant No. 14XNLQ07).

Tinene: a two-dimensional Dirac material with a 72 meV band gap.

Science.gov (United States)

Cai, Bo; Zhang, Shengli; Hu, Ziyu; Hu, Yonghong; Zou, Yousheng; Zeng, Haibo

2015-05-21

Dirac materials have attracted great interest for both fundamental research and electronic devices due to their unique band structures, but the usual near zero bandgap of graphene results in a poor on-off ratio in the corresponding transistors. Here, we report on tinene, monolayer gray tin, as a new two-dimensional material with both Dirac characteristics and a remarkable 72 meV bandgap based on density functional theory calculations. Compared with silicene and germanene, tinene has a similar hexagonal honeycomb monolayer structure, but it has an obviously larger buckling height (∼0.70 Å). Interestingly, such a moderate buckling structure results in phonon dispersion without appreciable imaginary modes, indicating the strong dynamic stability of tinene. Significantly, a distinct transformation is discovered from the band structure that six Dirac cones would appear at high symmetry K points in the first Brillouin zone when gray tin is thinned from the bulk to monolayer, but a bandgap as large as 72 meV is still preserved. Considering the recent successful realization of silicene and germanene with a similar structure, the predicted stable tinene with Dirac characteristics and a suitable bandgap is a possibility for the "more than Moore" materials and devices.

Interacting fermions on a random lattice

International Nuclear Information System (INIS)

Perantonis, S.J.; Wheater, J.F.

1988-01-01

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and tehy decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and taht the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings. (orig.)

Instantons and Massless Fermions in Two Dimensions

Science.gov (United States)

Callan, C. G. Jr.; Dashen, R.; Gross, D. J.

1977-05-01

The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.

Feynman rules for fermion-number-violating interactions

International Nuclear Information System (INIS)

Denner, A.; Eck, H.; Hahn, O.; Kueblbeck, J.

1992-01-01

We present simple algorithmic Feynman rules for fermion-number-violating interactions. They do not involve explicit charge-conjugation matrices and resemble closely the familiar rules for Dirac fermions. We insist on a fermion flow through the graphs along fermion lines and get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions. We only need the familiar Dirac propagator and fewer vertices than in the usual treatment of fermion-number-violating interactions. (orig.)

Fermion masses from dimensional reduction

International Nuclear Information System (INIS)

Kapetanakis, D.; Zoupanos, G.

1990-01-01

We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.)

Fermion masses from dimensional reduction

Energy Technology Data Exchange (ETDEWEB)

Kapetanakis, D. (National Research Centre for the Physical Sciences Democritos, Athens (Greece)); Zoupanos, G. (European Organization for Nuclear Research, Geneva (Switzerland))

1990-10-11

We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.).

Rare-Region-Induced Avoided Quantum Criticality in Disordered Three-Dimensional Dirac and Weyl Semimetals

Directory of Open Access Journals (Sweden)

J. H. Pixley

2016-06-01

Full Text Available We numerically study the effect of short-ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed (and extensively theoretically studied quantum critical point separating semimetal and diffusive-metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian (H and exactly calculate the density of states (DOS near zero energy, using a combination of Lanczos on H^{2} and the kernel polynomial method on H. We establish the existence of two distinct types of low-energy eigenstates contributing to the disordered density of states in the weak-disorder semimetal regime. These are (i typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states and (ii nonperturbative rare eigenstates that are weakly dispersive and quasilocalized in the real-space regions with the largest (and rarest local random potential. Using twisted boundary conditions, we are able to systematically find and study these two (essentially independent types of eigenstates. We find that the Dirac states contribute low-energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasilocalized eigenstates contribute a nonzero background DOS which is only weakly energy dependent near zero energy and is exponentially small at weak disorder. We also find that the expected semimetal to diffusive-metal quantum critical point is converted to an avoided quantum criticality that is “rounded out” by nonperturbative effects, with no signs of any singular behavior in the DOS at the energy of the clean Dirac point. However, the crossover effects of the avoided (or hidden criticality manifest themselves in a so-called quantum critical fan region away from the Dirac energy. We discuss the implications of our results for

Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System α-(BEDT-TTF2I3

Directory of Open Access Journals (Sweden)

Daigo Ohki

2018-03-01

Full Text Available The optical conductivity in the charge order phase is calculated in the two-dimensional extended Hubbard model describing an organic Dirac electron system α -(BEDT-TTF 2 I 3 using the mean field theory and the Nakano-Kubo formula. Because the interband excitation is characteristic in a two-dimensional Dirac electron system, a peak structure is found above the charge order gap. It is shown that the peak structure originates from the Van Hove singularities of the conduction and valence bands, where those singularities are located at a saddle point between two Dirac cones in momentum space. The frequency of the peak structure exhibits drastic change in the vicinity of the charge order transition.

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

International Nuclear Information System (INIS)

Wang, Lei; Corboz, Philippe; Troyer, Matthias

2014-01-01

Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point V/t=1.356(1) with the critical exponents ν=0.80(3) and η=0.302(7). Compatible results for the transition point are also obtained with infinite projected entangled-pair states. (paper)

Two-loop Dirac neutrino mass and WIMP dark matter

OpenAIRE

Bonilla, Cesar; Ma, Ernest; Peinado, Eduardo; Valle, Jose W.F.

2018-01-01

We propose a "scotogenic" mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two--loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical $Diracon$ that induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhan...

Double valley Dirac fermions for 3D and 2D Hg1-x Cd x Te with strong asymmetry

Science.gov (United States)

Marchewka, M.

2017-04-01

In this paper the possibility to bring about the double-valley Dirac fermions in some quantum structures is predicted. These quantum structures are: strained 3D Hg1-x Cd x Te topological insulator (TI) with strong interface inversion asymmetry and the asymmetric Hg1-x Cd x Te double quantum wells (DQW). The numerical analysis of the dispersion relation for 3D TI Hg1-x Cd x Te for the proper Cd (x)-content of the Hg1-x Cd x Te compound clearly shows that the inversion symmetry breaking together with the unaxial tensile strain causes the splitting of each of the Dirac nodes (two belonging to two interfaces) into two in the proximity of the Γ-point. Similar effects can be obtained for asymmetric Hg1-x Cd x Te DQW with the proper content of Cd and proper width of the quantum wells. The aim of this work is to explore the inversion symmetry breaking in 3D TI and 2D DQW mixed HgCdTe systems. It is shown that this symmetry breaking leads to the dependence of carriers energy on quasi-momentum similar to that of Weyl fermions.

Interplay between topology and disorder in a two-dimensional semi-Dirac material

OpenAIRE

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2017-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one, and a parabolic dispersion in the orthogonal, direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi-metal, as it generates a momentum independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three dist...

Dirac fermions in blue-phosphorus

International Nuclear Information System (INIS)

Li, Yuanchang; Chen, Xiaobin

2014-01-01

We propose that Dirac cones can be engineered in phosphorene with fourfold-coordinated phosphorus atoms. The key is to separate the energy levels of the in-plane (s, p x , and p y ) and out-of-plane (p z ) oribtals through the sp 2 configuration, yielding respective σ- and π-character Dirac cones, and then quench the latter. As a proof-of-principle study, we create σ-character Dirac cones in hydrogenated and fluorinated phosphorene with a honeycomb lattice. The obtained Dirac cones are at K-points, slightly anisotropic, with Fermi velocities of 0.91 and 1.23 times that of graphene along the ΓK and KM direction, and maintain good linearity up to ∼2 eV for holes. A substantive advantage of a σ-character Dirac cone is its convenience in tuning the Dirac gap via in-plane strain. Our findings pave the way for development of high-performance electronic devices based on Dirac materials. (letter)

FLIC-overlap fermions and topology

International Nuclear Information System (INIS)

Kamleh, W.; Kusterer, D.J.; Leinweber, D.B.; Williams, A.G.

2003-01-01

APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F μν in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson Dirac operator associated with lattice artifacts at the scale of the lattice spacing are removed with FLIC fermions composed with an O(α 4 )-improved lattice field strength tensor. Hence, FLIC-Overlap fermions provide an additional benefit to the overlap formalism: a correct realization of topology in the fermion sector on the lattice

Anisotropic Weyl fermions from the quasiparticle excitation spectrum of a 3D Fulde-Ferrell superfluid.

Science.gov (United States)

Xu, Yong; Chu, Rui-Lin; Zhang, Chuanwei

2014-04-04

Weyl fermions, first proposed for describing massless chiral Dirac fermions in particle physics, have not been observed yet in experiments. Recently, much effort has been devoted to explore Weyl fermions around band touching points of single-particle energy dispersions in certain solid state materials (named Weyl semimetals), similar as graphene for Dirac fermions. Here we show that such Weyl semimetals also exist in the quasiparticle excitation spectrum of a three-dimensional spin-orbit-coupled Fulde-Ferrell superfluid. By varying Zeeman fields, the properties of Weyl fermions, such as their creation and annihilation, number and position, as well as anisotropic linear dispersions around band touching points, can be tuned. We study the manifestation of anisotropic Weyl fermions in sound speeds of Fulde-Ferrell fermionic superfluids, which are detectable in experiments.

Jordan-Wigner fermionization and the theory of low-dimensional quantum spin models

International Nuclear Information System (INIS)

Derzhko, O.

2007-01-01

The idea of mapping quantum spin lattice model onto fermionic lattice model goes back to Jordan and Wigner (1928) who transformed s = 1/2 operators which commute at different lattice sites into fermionic operators. Later on the Jordan-Wigner transformation was used for mapping one-dimensional s = 1/2 isotropic XY (XX) model onto an exactly solvable tight-binding model of spinless fermions (Lieb, Schultz and Mattis, 1961). Since that times the Jordan-Wigner transformation is known as a powerful tool in the condensed matter theory especially in the theory of low-dimensional quantum spin systems. The aim of these lectures is to review the applications of the Jordan-Wigner fermionization technique for calculating dynamic properties of low-dimensional quantum spin models. The dynamic quantities (such as dynamic structure factors or dynamic susceptibilities) are observable directly or indirectly in various experiments. The frequency and wave-vector dependence of the dynamic quantities yields valuable information about the magnetic structure of materials. Owing to a tremendous recent progress in synthesizing low-dimensional magnetic materials detailed comparisons of theoretical results with direct experimental observation are becoming possible. The lectures are organized as follows. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several low-dimensional quantum spin models. We start from a famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four-fermion

Three dimensional Dirac point at k=0 in photonic and phononic systems

OpenAIRE

Huang, Xueqin; Liu, Fengming; Chan, C. T.

2012-01-01

While "Dirac cone" dispersions can only be meaningfully defined in two dimensional (2D) systems, the notion of a Dirac point can be extended to three dimensional (3D) classical wave systems. We show that a simple cubic photonic crystal composing of core-shell spheres exhibits a 3D Dirac point at the center of the Brillouin zone at a finite frequency. Using effective medium theory, we can map our structure to a zero refractive index material in which the effective permittivity and permeability...

Quantum tunneling effect of Dirac particles in a Schwarzschild-Godel space-time

Energy Technology Data Exchange (ETDEWEB)

Qi, D.-J.; Li, S.-M., E-mail: qidejiang0504@126.com [Shenyang Inst. of Engineering, Shenyang (China); Ru, H.-Q. [Northeastern Univ., Shenyang (China)

2010-11-15

In this paper, motivated by the Kerner and Man fermion tunneling method of 4-dimensional black holes, we further improve the analysis to investigate the quantum tunneling effect of Dirac particles from the five-dimensional Schwarzschild-Godel black hole. We successfully construct a set of appropriate matrices γ{sup μ} for the general covariant Dirac equation and derive the tunneling probability and Hawking temperature, which is exactly the same as that obtained by other methods. (author)

Chiral-like tunneling of electrons in two-dimensional semiconductors with Rashba spin-orbit coupling.

Science.gov (United States)

Ang, Yee Sin; Ma, Zhongshui; Zhang, C

2014-01-21

The unusual tunneling effects of massless chiral fermions (mCF) and massive chiral fermions (MCF) in a single layer graphene and bilayer graphene represent some of the most bizarre quantum transport phenomena in condensed matter system. Here we show that in a two-dimensional semiconductor with Rashba spin-orbit coupling (R2DEG), the real-spin chiral-like tunneling of electrons at normal incidence simultaneously exhibits features of mCF and MCF. The parabolic branch of opposite spin in R2DEG crosses at a Dirac-like point and has a band turning point. These features generate transport properties not found in usual two-dimensional electron gas. Albeit its π Berry phase, electron backscattering is present in R2DEG. An electron mimics mCF if its energy is in the vicinity of the subband crossing point or it mimics MCF if its energy is near the subband minima.

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

International Nuclear Information System (INIS)

Yarmohammadi, Mohsen; Zareyan, Malek

2016-01-01

In graphene, conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature. For this reason, the bounding of electrons in graphene in the form of geometries of quantum dots is impossible. In gapless graphene, due to its unique electronic band structure, there is a minimal conductivity at Dirac points, that is, in the limit of zero doping. This creates a problem for using such a highly motivated new material in electronic devices. One of the ways to overcome this problem is the creation of a band gap in the graphene band structure, which is made by inversion symmetry breaking (symmetry of sublattices). We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for “local chemical potential” and “local gap”. The calculated energy spectrum exhibits quite different features with and without the perturbations. A characteristic equation for bound states (BSs) has been obtained. It is surprisingly found that the relation between the radial functions of sublattices wave functions, i.e., , , and , , can be established by SO (2) group. (paper)

Double Dirac Point Semimetal in Two-Dimensional Material: Ta2Se3

OpenAIRE

Ma, Yandong; Jing, Yu; Heine, Thomas

2017-01-01

Here, we report by first-principles calculations one new stable 2D Dirac material, Ta2Se3 monolayer. For this system, stable layered bulk phase exists, and exfoliation should be possible. Ta2Se3 monolayer is demonstrated to support two Dirac points close to the Fermi level, achieving the exotic 2D double Dirac semimetal. And like 2D single Dirac and 2D node-line semimetals, spin-orbit coupling could introduce an insulating state in this new class of 2D Dirac semimetals. Moreover, the Dirac fe...

Null-plane quantization of fermions

International Nuclear Information System (INIS)

Mustaki, D.

1990-01-01

Massive Dirac fermions are canonically quantized on the null plane using the Dirac-Bergmann algorithm. The procedure is carried out in the framework of quantum electrodynamics as an illustration of a rigorous treatment of interacting fermion fields

NLO+NLL collider bounds, Dirac fermion and scalar dark matter in the B-L model

Energy Technology Data Exchange (ETDEWEB)

Klasen, Michael [Westfaelische Wilhelms-Universitaet Muenster, Institut fuer Theoretische Physik, Muenster (Germany); Lyonnet, Florian [Southern Methodist University, Dallas, TX (United States); Queiroz, Farinaldo S. [Max-Planck-Institut fuer Kernphysik, Particle and Astroparticle Physics Division, Heidelberg (Germany)

2017-05-15

Baryon and lepton numbers being accidental global symmetries of the Standard Model (SM), it is natural to promote them to local symmetries. However, to preserve anomaly-freedom, only combinations of B-L are viable. In this spirit, we investigate possible dark matter realizations in the context of the U(1){sub B-L} model: (i) Dirac fermion with unbroken B-L; (ii) Dirac fermion with broken B-L; (iii) scalar dark matter; (iv) two-component dark matter. We compute the relic abundance, direct and indirect detection observables and confront them with recent results from Planck, LUX-2016, and Fermi-LAT and prospects from XENON1T. In addition to the well-known LEP bound M{sub Z}{sup {sub '}}/g{sub BL} >or similar 7 TeV, we include often ignored LHC bounds using 13 TeV dilepton (dimuon + dielectron) data at next-to-leading order plus next-to-leading logarithmic accuracy. We show that, for gauge couplings smaller than 0.4, the LHC gives rise to the strongest collider limit. In particular, we find M{sub Z}{sup {sub '}}/g{sub BL} > 8.7 TeV for g{sub BL} = 0.3. We conclude that the NLO+NLL corrections improve the dilepton bounds on the Z{sup '} mass and that both dark matter candidates are only viable in the Z{sup '} resonance region, with the parameter space for scalar dark matter being fully probed by XENON1T. Lastly, we show that one can successfully have a minimal two-component dark matter model. (orig.)

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

Science.gov (United States)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Alternative to domain wall fermions

International Nuclear Information System (INIS)

Neuberger, H.

2002-01-01

An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain wall fermions will in general be associated with a condition number that is of the same order of magnitude as the product of the condition number of the linear problem in the physical dimensions by the inverse bare quark mass. Thus, the computational cost of implementing true domain wall fermions using a single conjugate gradient algorithm is of the same order of magnitude as that of implementing the overlap Dirac operator directly using two nested conjugate gradient algorithms. At a cost of about a factor of two in operation count it is possible to make the memory usage of direct implementations of the overlap Dirac operator independent of the accuracy of the approximation to the sign function and of the same order as that of standard Wilson fermions

Particlelike solutions of the Einstein-Dirac equations

Science.gov (United States)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-05-01

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

Axial gravity, massless fermions and trace anomalies

International Nuclear Information System (INIS)

Bonora, L.; Cvitan, M.; Giaccari, S.; Stemberga, T.; Prester, P.D.; Pereira, A.D.; UFF-Univ. Federal Fluminense, Niteroi

2017-01-01

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)

Axial gravity, massless fermions and trace anomalies

Energy Technology Data Exchange (ETDEWEB)

Bonora, L. [International School for Advanced Studies (SISSA), Trieste (Italy); KEK, Tsukuba (Japan). KEK Theory Center; INFN, Sezione di Trieste (Italy); Cvitan, M.; Giaccari, S.; Stemberga, T. [Zagreb Univ. (Croatia). Dept. of Physics; Prester, P.D. [Rijeka Univ. (Croatia). Dept. of Physics; Pereira, A.D. [UERJ-Univ. Estadual do Rio de Janeiro (Brazil). Dept. de Fisica Teorica; UFF-Univ. Federal Fluminense, Niteroi (Brazil). Inst. de Fisica

2017-08-15

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

Science.gov (United States)

Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

2018-03-23

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera

Science.gov (United States)

Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

2018-03-01

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting—henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Interfacial Dirac cones from alternating topological invariant superlattice structures of Bi2Se3.

Science.gov (United States)

Song, Jung-Hwan; Jin, Hosub; Freeman, Arthur J

2010-08-27

When the three-dimensional topological insulators Bi2Se3 and Bi2Te3 have an interface with vacuum, i.e., a surface, they show remarkable features such as topologically protected and spin-momentum locked surface states. However, for practical applications, one often requires multiple interfaces or channels rather than a single surface. Here, for the first time, we show that an interfacial and ideal Dirac cone is realized by alternating band and topological insulators. The multichannel Dirac fermions from the superlattice structures open a new way for applications such as thermoelectric and spintronics devices. Indeed, utilizing the interfacial Dirac fermions, we also demonstrate the possible power factor improvement for thermoelectric applications.

Clifford Algebra Implying Three Fermion Generations Revisited

International Nuclear Information System (INIS)

Krolikowski, W.

2002-01-01

The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √p 2 → Γ (N) ·p works, leading to a sequence N=1, 2, 3, ... of Dirac-type equations, where four Dirac-type matrices Γ (N) μ are embedded into a Clifford algebra via a Jacobi definition introducing four ''centre-of-mass'' and (N - 1) x four ''relative'' Dirac-type matrices. These define one ''centre-of-mass'' and N - 1 ''relative'' Dirac bispinor indices. Secundo, the ''centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while N - 1 ''relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ''relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1, 3, 5 in the case of N odd, and two with N = 2, 4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3 x 3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is m τ = 1776.80 MeV, when the input of experimental m e and m μ is used. (author)

Clifford Algebra Implying Three Fermion Generations Revisited

Science.gov (United States)

Krolikowski, Wojciech

2002-09-01

The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √ {p2} → {Γ }(N)p works, leading to a sequence N = 1,2,3, ... of Dirac-type equations, where four Dirac-type matrices {Γ }(N)μ are embedded into a Clifford algebra via a Jacobi definition introducing four ``centre-of-mass'' and (N-1)× four ``relative'' Dirac-type matrices. These define one ``centre-of-mass'' and (N-1) ``relative'' Dirac bispinor indices. Secundo, the ``centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while (N-1) ``relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ``relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1,3,5 in the case of N odd, and two with N = 2,4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3x3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is mτ = 1776.80 MeV, when the input of experimental me and mμ is used.

Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors

International Nuclear Information System (INIS)

Bocquet, M.; Serban, D.; Zirnbauer, M.R.

2000-01-01

Disordered noninteracting quasiparticles that are governed by a Majorana-type Hamiltonian -- prominent examples are dirty superconductors with broken time-reversal and spin-rotation symmetry, or the fermionic representation of the 2d Ising model with fluctuating bond strengths -- are called class D . In two dimensions, weakly disordered systems of this kind may possess a metallic phase beyond the insulating phases expected for strong disorder. We show that the 2d metal phase emanates from the free Majorana fermion point, in the direction of the RG trajectory of a perturbed WZW model. To establish this result, we develop a supersymmetric extension of the method of nonabelian bosonization. On the metallic side of the metal-insulator transition, the density of states becomes nonvanishing at zero energy, by a mechanism akin to dynamical mass generation. This feature is explored in a model of N species of disordered Dirac fermions, via the mapping on a nonlinear sigma model, which encapsulates a Z 2 spin degree of freedom. We compute the density of states in a finite system, and obtain agreement with the random-matrix prediction for class D , in the ergodic limit. Vortex disorder, which is a relevant perturbation at the free-fermion point, changes the density of states at low energy and suppresses the local Z 2 degree of freedom, thereby leading to a different symmetry class, BD

Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

Science.gov (United States)

Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.

2018-04-01

We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.

Disorder effects in two-dimensional Fermi systems with conical spectrum: exact results for the density of states

International Nuclear Information System (INIS)

Nersesyan, A.A.; Tsvelik, A.M.; Wenger, F.

1995-01-01

The influence of weak non-magnetic disorder on the single-particle density of states ρ(ω) of two-dimensional electron systems with a conical spectrum is studied. We use a non-perturbative approach, based on the replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by abelian and non-abelian bosonization methods. Specifically, we consider a weakly disordered p- or d-wave superconductor, in which case the problem reduces to a model of (2+1)-dimensional massless Dirac fermions coupled to random, static, generally non-abelian gauge fields. It is shown that the density of states of a two-dimensional p- or d-wave superconductor, averaged over randomness, follows a non-trivial power-law behavior near the Fermi energy: ρ(ω) similar vertical stroke ωvertical stroke α . The exponent α>0 is exactly calculated for several types of disorder. We demonstrate that the property ρ(0) = 0 is a direct consequence of a continuous symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we also discuss another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite ρ(0) due to the breakdown of a discrete (particle-hole) symmetry. ((orig.))

Studies of Dirac and Weyl fermions by angle resolved photoemission spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Huang, Lunan [Iowa State Univ., Ames, IA (United States)

2016-01-01

This dissertation consists of three parts. First, we study magnetic domains in Nd₂Fe₁₄B single crystals using high resolution magnetic force microscopy (MFM). In addition to the elongated, wavy nano-domains reported by a previous MFM study, we found that the micrometer size, star-shaped fractal pattern is constructed of an elongated network of nano-domains about 20 nm in width, with resolution-limited domain walls thinner than 2 nm. Second, we studied extra Dirac cones of multilayer graphene on SiC surface by ARPES and SPA-LEED. We discovered extra Dirac cones on Fermi surface due to SiC 6 x 6 and graphene 6√ 3 6√ 3 coincidence lattice on both single-layer and three-layer graphene sheets. We interpreted the position and intensity of the Dirac cone replicas, based on the scattering vectors from LEED patterns. We found the positions of replica Dirac cones are determined mostly by the 6 6 SiC superlattice even graphene layers grown thicker. Finally, we studied the electronic structure of MoTe₂ by ARPES and experimentally con rmed the prediction of type II Weyl state in this material. By combining the result of Density Functional Theory calculations and Berry curvature calculations with out experimental data, we identi ed Fermi arcs, track states and Weyl points, all features predicted to exist in a type II Weyl semimetal. This material is an excellent playground for studies of exotic Fermions.

Fermions in five-dimensional brane world models

Energy Technology Data Exchange (ETDEWEB)

Smolyakov, Mikhail N. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,119991, Moscow (Russian Federation)

2016-06-28

In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.

Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems

Science.gov (United States)

Milletarı, Mirco; Offidani, Manuel; Ferreira, Aires; Raimondi, Roberto

2017-12-01

We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin-valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies.

Electronic structure, Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na3Bi from angle-resolved photoemission spectroscopy

International Nuclear Information System (INIS)

Liang Aiji; Chen Chaoyu; Wang Zhijun; Shi Youguo; Feng Ya; Yi Hemian; Xie Zhuojin; He Shaolong; He Junfeng; Peng Yingying; Liu Yan; Liu Defa; Hu Cheng; Zhao Lin; Liu Guodong; Dong Xiaoli; Zhang Jun; Nakatake, M; Iwasawa, H; Shimada, K

2016-01-01

The three-dimensional (3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A 3 Bi ( A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission (ARPES) measurements on the two cleaved surfaces, (001) and (100), of Na 3 Bi. On the (001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k x – k y plane and by varying the photon energy to get access to different out-of-plane k z s. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the (100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the (100) plane. We directly observe two isolated 3D Dirac nodes on the (100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ∼150 meV before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na 3 Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the 3D Dirac cones, on the possible formation of surface reconstruction of the (001) surface, and on the issue of basic Brillouin zone selection for the (100) surface. (rapid communication)

Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry

Directory of Open Access Journals (Sweden)

E. Kalesaki

2014-01-01

Full Text Available We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial flat bands and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the π-π^{⋆} band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene; they combine a Dirac cone and flat bands because of their P-orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

International Nuclear Information System (INIS)

Toublan, D.; Verbaarschot, J.J.M.

1999-01-01

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N f → Sp (2N f ) and SU (N f → O (N f ), respectively, rather than the symmetry breaking pattern SU (N f ) x SU (N f ) → SU (N f ) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 2 Λ QCD (wing L the linear size of the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator

Kondo effect in three-dimensional Dirac and Weyl systems

NARCIS (Netherlands)

Mitchell, Andrew K.; Fritz, Lars

2015-01-01

Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a

Observation of three-component fermions in the topological semimetal molybdenum phosphide

Science.gov (United States)

Lv, B. Q.; Feng, Z.-L.; Xu, Q.-N.; Gao, X.; Ma, J.-Z.; Kong, L.-Y.; Richard, P.; Huang, Y.-B.; Strocov, V. N.; Fang, C.; Weng, H.-M.; Shi, Y.-G.; Qian, T.; Ding, H.

2017-06-01

In quantum field theory, Lorentz invariance leads to three types of fermion—Dirac, Weyl and Majorana. Although the existence of Weyl and Majorana fermions as elementary particles in high-energy physics is debated, all three types of fermion have been proposed to exist as low-energy, long-wavelength quasiparticle excitations in condensed-matter systems. The existence of Dirac and Weyl fermions in condensed-matter systems has been confirmed experimentally, and that of Majorana fermions is supported by various experiments. However, in condensed-matter systems, fermions in crystals are constrained by the symmetries of the 230 crystal space groups rather than by Lorentz invariance, giving rise to the possibility of finding other types of fermionic excitation that have no counterparts in high-energy physics. Here we use angle-resolved photoemission spectroscopy to demonstrate the existence of a triply degenerate point in the electronic structure of crystalline molybdenum phosphide. Quasiparticle excitations near a triply degenerate point are three-component fermions, beyond the conventional Dirac-Weyl-Majorana classification, which attributes Dirac and Weyl fermions to four- and two-fold degenerate points, respectively. We also observe pairs of Weyl points in the bulk electronic structure of the crystal that coexist with the three-component fermions. This material thus represents a platform for studying the interplay between different types of fermions. Our experimental discovery opens up a way of exploring the new physics of unconventional fermions in condensed-matter systems.

A Dirac-Kaehler approach to the two dimensional Wess-Zumino N=2 model on the lattice

International Nuclear Information System (INIS)

Zimerman, A.H.; Aratyn, H.

1983-08-01

We introduce a Dirac-Kaehler model for the two dimensional Wess-Zumino N=2 Lagrangean. We can show that in the model, when we go to the euclidean space-time lattive, we have no energy doubling, the action has no lattice surface terms (contrary to other authors), while the Hamiltonians (when time is continuous) present lattice surface terms. (orig.)

Graphene based d-character Dirac Systems

Science.gov (United States)

Li, Yuanchang; Zhang, S. B.; Duan, Wenhui

From graphene to topological insulators, Dirac material continues to be the hot topics in condensed matter physics. So far, almost all of the theoretically predicted or experimentally observed Dirac materials are composed of sp -electrons. By using first-principles calculations, we find the new Dirac system of transition-metal intercalated epitaxial graphene on SiC(0001). Intrinsically different from the conventional sp Dirac system, here the Dirac-fermions are dominantly contributed by the transition-metal d-electrons, which paves the way to incorporate correlation effect with Dirac-cone physics. Many intriguing quantum phenomena are proposed based on this system, including quantum spin Hall effect with large spin-orbital gap, quantum anomalous Hall effect, 100% spin-polarized Dirac fermions and ferromagnet-to-topological insulator transition.

Hofstadter's butterfly energy spectrum of ultracold fermions on the two-dimensional triangular optical lattice

International Nuclear Information System (INIS)

Hou Jingmin; Lu Qingqing

2009-01-01

We study the energy spectrum of ultracold fermionic atoms on the two-dimensional triangular optical lattice subjected to a perpendicular effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations and numerically solve them, then we obtain the Hofstadter's butterfly-like energy spectrum, which has a novel fractal structure. The observability of the Hofstadter's butterfly spectrum is also discussed

Two-dimensional Yukawa interactions from nonlocal Proca quantum electrodynamics

Science.gov (United States)

Alves, Van Sérgio; Macrı, Tommaso; Magalhães, Gabriel C.; Marino, E. C.; Nascimento, Leandro O.

2018-05-01

We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle, which may be either scalar or an abelian gauge field, both of them in (3 +1 ) dimensions. Thereafter, we consider that the fermionic matter field propagates only in (2 +1 ) dimensions, whereas the bosonic field is free to propagate out of the plane. Within these assumptions, we apply a mechanism for dimensional reduction, which yields an effective model in (2 +1 ) dimensions. In particular, for the gauge-field case, we use the Stueckelberg mechanism in order to preserve gauge invariance. We refer to this version as nonlocal-Proca quantum electrodynamics (NPQED). For both scalar and gauge cases, the effective models reproduce the usual Yukawa interaction in the static limit. By means of perturbation theory at one loop, we calculate the mass renormalization of the Dirac field. Our model is a generalization of Pseudo quantum electrodynamics (PQED), which is a gauge-field model that provides a Coulomb interaction for two-dimensional electrons. Possibilities of application to Fermi-Bose mixtures in mixed dimensions, using cold atoms, are briefly discussed.

Electronic structure engineering in silicene via atom substitution and a new two-dimensional Dirac structure Si3C

Science.gov (United States)

Yin, Na; Dai, Ying; Wei, Wei; Huang, Baibiao

2018-04-01

A lot of efforts have been made towards the band gap opening in two-dimensional silicene, the silicon version of graphene. In the present work, the electronic structures of single atom doped (B, N, Al and P) and codoped (B/N and Al/P) silicene monolayers are systematically examined on the base of density functional electronic calculations. Our results demonstrate that single atom doping can realize electron or hole doping in the silicene; while codoping, due to the syergistic effects, results in finite band gap in silicene at the Dirac point without significantly degrading the electronic properties. In addition, the characteristic of band gap shows dependence on the doping concentration. Importantly, we predict a new two-dimensional Dirac structure, the graphene-like Si3C, which also shows linear band dispersion relation around the Fermi level. Our results demonstrates an important perspective to engineer the electronic and optical properties of silicene.

Collective modes of massive Dirac fermions in armchair graphene nanoribbons

International Nuclear Information System (INIS)

Andersen, David R; Raza, Hassan

2013-01-01

We report the plasmon dispersion characteristics of intrinsic and extrinsic armchair graphene nanoribbons of atomic width N = 5 using a p z -orbital tight binding model with third-nearest-neighbor (3nn) coupling. The hopping parameters are obtained by fitting the 3nn dispersions to those of an extended Hückel theory. The resultant massive Dirac fermion system has a band gap E g ≈ 64 meV. The extrinsic plasmon dispersion relation is found to asymptotically approach a universal dispersion curve as the chemical potential μ increases, whereas the intrinsic plasmon dispersion relation is found to have both energy and momentum thresholds. We also report an analytical model for the extrinsic plasmon group velocity in the q → 0 limit.

A two-dimensional Dirac fermion microscope

DEFF Research Database (Denmark)

Bøggild, Peter; Caridad, Jose; Stampfer, Christoph

2017-01-01

D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges...

Two-dimensional thermofield bosonization II: Massive fermions

International Nuclear Information System (INIS)

Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

2008-01-01

We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield formulation. Thereby we establish in thermofield dynamics the formal equivalence of the massive free fermion theory with the sine-Gordon thermofield model for a particular value of the sine-Gordon parameter. We extend the thermofield bosonization to include the massive Thirring model

Scanning Tunnelling Spectroscopic Studies of Dirac Fermions in Graphene and Topological Insulators

Directory of Open Access Journals (Sweden)

wang K.-L.

2012-03-01

Full Text Available We report novel properties derived from scanning tunnelling spectroscopic (STS studies of Dirac fermions in graphene and the surface state (SS of a strong topological insulator (STI, Bi2Se3. For mono-layer graphene grown on Cu by chemical vapour deposition (CVD, strain-induced scalar and gauge potentials are manifested by the charging effects and the tunnelling conductance peaks at quantized energies, respectively. Additionally, spontaneous time-reversal symmetry breaking is evidenced by the alternating anti-localization and localization spectra associated with the zero-mode of two sublattices while global time-reversal symmetry is preserved under the presence of pseudo-magnetic fields. For Bi2Se3 epitaxial films grown on Si(111 by molecular beam epitaxy (MBE, spatially localized unitary impurity resonances with sensitive dependence on the energy difference between the Fermi level and the Dirac point are observed for samples thicker than 6 quintuple layers (QL. These findings are characteristic of the SS of a STI and are direct manifestation of strong topological protection against impurities. For samples thinner than 6-QL, STS studies reveal the openup of an energy gap in the SS due to overlaps of wave functions between the surface and interface layers. Additionally, spin-preserving quasiparticle interference wave-vectors are observed, which are consistent with the Rashba-like spin-orbit splitting.

Landau-level spectroscopy of massive Dirac fermions in single-crystalline ZrTe5 thin flakes

Science.gov (United States)

Jiang, Y.; Dun, Z. L.; Zhou, H. D.; Lu, Z.; Chen, K.-W.; Moon, S.; Besara, T.; Siegrist, T. M.; Baumbach, R. E.; Smirnov, D.; Jiang, Z.

2017-07-01

We report infrared magnetospectroscopy studies on thin crystals of an emerging Dirac material ZrTe5 near the intrinsic limit. The observed structure of the Landau-level transitions and zero-field infrared absorption indicate a two-dimensional Dirac-like electronic structure, similar to that in graphene but with a small relativistic mass corresponding to a 9.4-meV energy gap. Measurements with circularly polarized light reveal a significant electron-hole asymmetry, which leads to splitting of the Landau-level transitions at high magnetic fields. Our model, based on the Bernevig-Hughes-Zhang effective Hamiltonian, quantitatively explains all observed transitions, determining the values of the Fermi velocity, Dirac mass (or gap), electron-hole asymmetry, and electron and hole g factors.

Three-dimensional periodic dielectric structures having photonic Dirac points

Science.gov (United States)

Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin

2015-06-02

The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.

Three-dimensional periodic dielectric structures having photonic Dirac points

Energy Technology Data Exchange (ETDEWEB)

Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin

2015-06-02

The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.

On the conductivity of a one-dimensional system of interacting fermions in a random potential

International Nuclear Information System (INIS)

Apel, W.

1981-01-01

A one-dimensional system of interacting fermions in an external potential is studied. The problem was for this purpose transformed to two classical models of statistical mechanics in two dimensions in which occasionally results were found in complementary ranges of the interaction constants of the fermion system. The conductivity appeared as a simple correlation function in both classical models. It was shown that the interaction in a one-dimensional polluted fermion system can cause an isolator-metal transition. (orig./HSI) [de

Dirac equation in 5- and 6-dimensional curved space-time manifolds

International Nuclear Information System (INIS)

Vladimirov, Yu.S.; Popov, A.D.

1984-01-01

The program of plotting unified multidimensional theory of gravitation, electromagnetism and electrically charged matter with transition from 5-dimensional variants to 6-dimensional theory possessing signature (+----+) is developed. For recording the Dirac equation in 5- and 6-dimensional curved space-time manifolds the tetrad formalism and γ-matrix formulation of the General Relativity Theory are used. It is shown that the 6-dimensional theory case unifies the two private cases of 5-dimensional theory and corresponds to two possibilities of the theory developed by Kadyshevski

Transport of Dirac fermions on the surface of strong topological insulator and graphene

Energy Technology Data Exchange (ETDEWEB)

Kundu, Arijit

2012-06-14

estimates covering the full temperature range are provided for the parameters of Bi{sub 2}Se{sub 3} which possibly can be verified by experiment. Afterwards, a theory of quantum transport and scattering by spatially localized static magnetic fields is developed in a unified way for the low energy Dirac Fermions on topological insulator and graphene. The employed model describes in a unified manner the effects of orbital magnetic fields, Zeeman and exchange fields in topological insulators, and the pseudo-magnetic fields caused by strain or defects in monolayer graphene. The general scattering theory is formulated, and for radially symmetric fields, the scattering amplitude and the total and transport cross sections are expressed in terms of phase shifts. As applications, I study ring-shaped magnetic fields. The Aharonov-Bohm geometry is also studied as a limit to the ring geometry. I also review the superconducting proximity effect on graphene and study resonant tunneling through a superconducting double barrier structure in graphene as a function of the system parameters. In this geometry, transmission resonances occur because of the formation of Andreev bound states. The evolution of the transport through this geometry as a function of the incident energy for various angles of incidence shows the damping of the resonance as normal reflection between the barriers increases. I also consider the phenomenon of quantum charge pumping of electrons in this geometry in the adiabatic limit. Quantum charge pumping can be achieved by modulating the amplitudes (Δ{sub 1} and Δ{sub 2}) of the gaps associated with the two superconducting strips. Because of transmission resonances in the Δ{sub 1} - Δ{sub 2} plane of parameter space, a large value of pumped charge is obtained when the pumping contour encloses the resonances. This is in sharp contrast to the case of charge pumping in a normal double barrier structure in graphene, where the pumped charge is very small, due to the

Phase diagram and Chiral Magnetic Effect in Dirac Semimetals from Lattice Simulation

Directory of Open Access Journals (Sweden)

Boyda D.L.

2018-01-01

Full Text Available Dirac Semimetals Na3Bi and Cd3As2 are recently discovered materials, which low energy electronic spectrum is described by two flavours of massless 3+1D fermions. In order to study electronic properties of these materials we formulated lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reproduces effective theory of Dirac semimetals. Using the lattice field theory we study the phase diagram of Dirac semimetals in the plane effective coupling constant - Fermi velocity anisotropy. We also measure conductivity of Dirac Semimetals within lattice field theory in external magnetic field. Our results confirm the existence of Chiral Magnetic Effect in Dirac Semimetals.

Running coupling in SU(2) gauge theory with two adjoint fermions

DEFF Research Database (Denmark)

Rantaharju, Jarno; Rantalaiho, Teemu; Rummukainen, Kari

2016-01-01

We study SU(2) gauge theory with two Dirac fermions in the adjoint representation of the gauge group on the lattice. Using clover improved Wilson fermion action with hypercubic truncated stout smearing we perform simulations at larger coupling than before. We measure the evolution of the coupling...... with the existence of a fixed point in the interval 2.2g∗23. We also measure the anomalous dimension and find that its value at the fixed point is γ∗≃0.2±0.03....... constant using the step scaling method with the Schrödinger functional and study the remaining discretization effects. At weak coupling we observe significant discretization effects, which make it difficult to obtain a fully controlled continuum limit. Nevertheless, the data remains consistent...

Interplay between topology and disorder in a two-dimensional semi-Dirac material

Science.gov (United States)

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2018-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes—single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

Pure quasifree states of the Dirac field from the fermionic projector

International Nuclear Information System (INIS)

Fewster, Christopher J; Lang, Benjamin

2015-01-01

We consider the quantized free massive Dirac field on oriented and globally hyperbolic ultrastatic slab spacetimes with compact spatial section and demonstrate how a gauge invariant, pure and quasifree state on the C*-completion of the self-dual CAR-algebra can be extracted from the fermionic projector construction of Finster and Reintjes. This state is analogous to the ‘SJ-state’ of the free scalar field recently discussed in the literature. We prove that this state generically fails to be Hadamard. However, we also show how a modified version of the construction, inspired by the work of Brum and Fredenhagen, yields states that are Hadamard. We also relate the Hadamard condition to the finiteness of fluctuations of Wick polynomials. (paper)

Voltage-induced switching of an antiferromagnetically ordered topological Dirac semimetal

Science.gov (United States)

Kim, Youngseok; Kang, Kisung; Schleife, André; Gilbert, Matthew J.

2018-04-01

An antiferromagnetic semimetal has been recently identified as a new member of topological semimetals that may host three-dimensional symmetry-protected Dirac fermions. A reorientation of the Néel vector may break the underlying symmetry and open a gap in the quasiparticle spectrum, inducing the (semi)metal-insulator transition. Here, we predict that such a transition may be controlled by manipulating the chemical potential location of the material. We perform both analytical and numerical analysis on the thermodynamic potential of the model Hamiltonian and find that the gapped spectrum is preferred when the chemical potential is located at the Dirac point. As the chemical potential deviates from the Dirac point, the system shows a possible transition from the gapped to the gapless phase and switches the corresponding Néel vector configuration. We perform density functional theory calculations to verify our analysis using a realistic material and discuss a two terminal transport measurement as a possible route to identify the voltage-induced switching of the Néel vector.

Three-dimensional topological insulators and bosonization

Energy Technology Data Exchange (ETDEWEB)

Cappelli, Andrea [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Randellini, Enrico [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Dipartimento di Fisica e Astronomia, Università di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Sisti, Jacopo [Scuola Internazionale Superiore di Studi Avanzati (SISSA),Via Bonomea 265, 34136 Trieste (Italy)

2017-05-25

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

Exact one-fermion-loop contributions in (1+1)-dimensional solitons

International Nuclear Information System (INIS)

Shepard, J.R.; Price, C.E.; Ferree, T.C.

1993-01-01

We find solutions to the (1+1)-dimensional scalar-only linear σ model. A new method is used to compute one-fermion-loop contributions exactly, and agreemment with published results employing other methods is excellent. A renormalization scheme which differs from that commonly used in such calculations but is similar to that required in 1+3 dimensions is also presented. We compare ''kink'' versus ''shallow bag'' solutions, paying careful attention to the implications of the one-fermion-loop contributions for the stability of the former. We find that, for small fermion multiplicities, self-consistent shallow bag solutions are always more bound than their metastable kink counterparts. However, as the fermion multiplicity increases, shallow bags evolve into kinks which eventually are the only self-consistent configurations. This situation is qualitatively the same for the two renormalization schemes considered. When we construct ''baryons,'' each containing three fermions, the kink configuration is typically more bound than the shallow bag when one-fermion-loop contributions are included

Three-dimensional Majorana fermions in chiral superconductors.

Science.gov (United States)

Kozii, Vladyslav; Venderbos, Jörn W F; Fu, Liang

2016-12-01

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs 4 Sb 12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Dynamical Symmetries of Two-Dimensional Dirac Equation with Screened Coulomb and Isotropic Harmonic Oscillator Potentials

International Nuclear Information System (INIS)

Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen

2014-01-01

In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)

Diffusion in higher dimensional SYK model with complex fermions

Science.gov (United States)

Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

2018-01-01

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

Integrating out the Dirac sea

International Nuclear Information System (INIS)

Karbstein, Felix

2009-01-01

We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''π meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)

Single-time reduction of bethe-salpeter formalism for two-fermion system

International Nuclear Information System (INIS)

Arkhipov, A.A.

1988-01-01

The single-time reduction method proposed in other refs. for the system of two scalar particles is generalized for the case of two-fermion system. A self-consistent procedure of single-time reduction has been constructed both in terms of the Bethe-Salpeter wave function and in terms of the Green's function of two-fermion system. Three-dimensional dynamic equations have been obtained for single-time wave functions and two-time Green's functions of a two-fermion system and the Schroedinger structure of the equations obtained is shown to be a consequence of the causality structure of the local QFT. 32 refs

General solution of the Dirac equation for quasi-two-dimensional electrons

Energy Technology Data Exchange (ETDEWEB)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

2016-06-15

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

Topological insulators Dirac equation in condensed matter

CERN Document Server

Shen, Shun-Qing

2017-01-01

This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already b...

Quantum confinement and heavy surface states of Dirac fermions in bismuth (111) films: An analytical approach

Science.gov (United States)

Enaldiev, V. V.; Volkov, V. A.

2018-03-01

Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is a topologically nontrivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near the M ¯ point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in the Γ ¯-M ¯ direction order of ten free electron masses and light effective mass in the M ¯-K ¯ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not split. In such a symmetric film with arbitrary thickness, the bottom of the lowest quantum confinement subband in the conduction band coincides with the bottom of the bulk conduction band in the M ¯ point.

Unquenched Complex Dirac Spectra at Nonzero Chemical Potential: Two-Color QCD Lattice Data versus Matrix Model

International Nuclear Information System (INIS)

Akemann, Gernot; Bittner, Elmar

2006-01-01

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses

A Dirac algebraic approach to supersymmetry

International Nuclear Information System (INIS)

Guersey, F.

1984-01-01

The power of the Dirac algebra is illustrated through the Kaehler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5,1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields. (author)

Anisotropic spin motive force in multi-layered Dirac fermion system, α-(BEDT-TTF)2I3

International Nuclear Information System (INIS)

Kubo, K; Morinari, T

2015-01-01

We investigate the anisotropic spin motive force in α-(BEDT-TTF) 2 I 3 , which is a multi-layered massless Dirac fermion system under pressure. Assuming the interlayer antiferromagnetic interaction and the interlayer anisotropic ferromagnetic interaction, we numerically examine the spin ordered state of the ground state using the steepest descent method. The anisotropic interaction leads to the anisotropic spin ordered state. We calculate the spin motive force produced by the anisotropic spin texture. The result quantitatively agrees with the experiment. (paper)

Thermalization of fermionic quantum fields

International Nuclear Information System (INIS)

Berges, Juergen; Borsanyi, Szabolcs; Serreau, Julien

2003-01-01

We solve the nonequilibrium dynamics of a (3+1)-dimensional theory with Dirac fermions coupled to scalars via a chirally invariant Yukawa interaction. The results are obtained from a systematic coupling expansion of the 2PI effective action to lowest nontrivial order, which includes scattering as well as memory and off-shell effects. The dynamics is solved numerically without further approximation, for different far-from-equilibrium initial conditions. The late-time behavior is demonstrated to be insensitive to the details of the initial conditions and to be uniquely determined by the initial energy density. Moreover, we show that at late time the system is very well characterized by a thermal ensemble. In particular, we are able to observe the emergence of Fermi-Dirac and Bose-Einstein distributions from the nonequilibrium dynamics

A Route to Dirac Liquid Theory: A Fermi Liquid Description for Dirac Materials

Science.gov (United States)

Gochan, Matthew; Bedell, Kevin

Since the pioneering work developed by L.V. Landau sixty years ago, Fermi Liquid Theory has seen great success in describing interacting Fermi systems. While much interest has been generated over the study of non-Fermi Liquid systems, Fermi Liquid theory serves as a formidable model for many systems and offers a rich amount of of results and insight. The recent classification of Dirac Materials, and the lack of a unifying theoretical framework for them, has motivated our study. Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, graphene, is the focus of this work. We present our Fermi Liquid description of Graphene. We find many interesting results, specifically in the transport and dynamics of the system. Additionally, we expand on previous work regarding the Virial Theorem and its impact on the Fermi Liquid parameters in graphene. Finally, we remark on viscoelasticity of Dirac Materials and other unusual results that are consequences of AdS-CFT.

Minimally doubled fermions and spontaneous chiral symmetry breaking

Directory of Open Access Journals (Sweden)

Osmanaj (Zeqirllari Rudina

2018-01-01

Full Text Available Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

Minimally doubled fermions and spontaneous chiral symmetry breaking

Science.gov (United States)

Osmanaj (Zeqirllari), Rudina; Hyka (Xhako), Dafina

2018-03-01

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks - Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss - Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

Quasi-relativistic fermions and dynamical flavour oscillations

CERN Document Server

Alexandre, Jean; Mavromatos, Nick E.

2014-01-01

We introduce new Lorentz-symmetry violating kinematics for a four-fermion interaction model, where dynamical mass generation is allowed, irrespectively of the strength of the coupling. In addition, these kinematics lead to a quasi-relativistic dispersion relation, in the sense that it is relativistic in both the infrared and the ultraviolet, but not in an intermediate regime, characterized by the mass $M$. For two fermions, we show that a flavour-mixing mass matrix is generated dynamically, and the Lorentz symmetric limit $M\\to\\infty$ leads to two free relativistic fermions, with flavour oscillations. This model, valid for either Dirac or Majorana fermions, can describe any set of phenomenological values for the eigen masses and the mixing angle.

Electrical manipulation of dynamic magnetic impurity and spin texture of helical Dirac fermions

Science.gov (United States)

Wang, Rui-Qiang; Zhong, Min; Zheng, Shi-Han; Yang, Mou; Wang, Guang-Hui

2016-05-01

We have theoretically investigated the spin inelastic scattering of helical electrons off a high-spin nanomagnet absorbed on a topological surface. The nanomagnet is treated as a dynamic quantum spin and driven by the spin transfer torque effect. We proposed a mechanism to electrically manipulate the spin texture of helical Dirac fermions rather than by an external magnetic field. By tuning the bias voltage and the direction of impurity magnetization, we present rich patterns of spin texture, from which important fingerprints exclusively associated with the spin helical feature are obtained. Furthermore, it is found that the nonmagnetic potential can create the resonance state in the spin density with different physics as the previously reported resonance of charge density.

Two-dimensional topological photonic systems

Science.gov (United States)

Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

2017-09-01

The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

One dimensional Dirac-Moshinsky oscillator-like system and isospectral partners

International Nuclear Information System (INIS)

Contreras-Astorga, A

2015-01-01

Two different exactly solvable systems are constructed using the supersymmetric quantum mechanics formalism and a pseudoscalar one-dimensional version of the Dirac- Moshinsky oscillator as a departing system. One system is built using a first-order SUSY transformation. The second is obtained through the confluent supersymmetry algorithm. The two of them are explicitly designed to have the same spectrum as the departing system and pseudoscalar potentials. (paper)

Fermion production despite fermion number conservation

International Nuclear Information System (INIS)

Bock, W.; Hetrick, J.E.; Smit, J.

1995-01-01

Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. Both the sharp momentum cutoff and the lattice regulator break gauge invariance. In the case of the lattice model a mass counterterm for the gauge field is sufficient to restore gauge invariance in the perturbative regime. A study of the vacuum energy shows however that the perturbative counterterm is insufficient in a nonperturbative setting and that further quartic counterterms are needed. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories. ((orig.))

Density functional theory investigation of two-dimensional dipolar fermions in a harmonic trap

International Nuclear Information System (INIS)

Ustunel, Hande; Abedinpour, Saeed H; Tanatar, B

2014-01-01

We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems

A Dirac sea pilot-wave model for quantum field theory

International Nuclear Information System (INIS)

Colin, S; Struyve, W

2007-01-01

We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and applies to the regime in which fermion number is superselected. This work is a further elaboration of work by Colin, in which a Dirac sea pilot-wave model is presented for quantum electrodynamics. We extend his work to non-electromagnetic interactions, we discuss a cut-off regularization of the pilot-wave model and study how it reproduces the standard quantum predictions. The Dirac sea pilot-wave model can be seen as a possible continuum generalization of a lattice model by Bell. It can also be seen as a development and generalization of the ideas by Bohm, Hiley and Kaloyerou, who also suggested the use of the Dirac sea for the development of a pilot-wave model for quantum electrodynamics

Majorana fermion exchange in strictly one dimensional structures

OpenAIRE

Chiu, Ching-Kai; Vazifeh, M. M.; Franz, M.

2014-01-01

It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of "Majorana shuttle" whereby a $\\pi$ domain wall in the superconducting order parameter which hosts a pair of ancillary Majoranas delivers one zero mode across the wire while the other one tunnels in ...

Spin-1 Dirac-Weyl fermions protected by bipartite symmetry

Energy Technology Data Exchange (ETDEWEB)

Lin, Zeren [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); School of Physics, Peking University, Beijing 100871 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)

2015-12-07

We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.

A comparative study of Dirac quasinormal modes of charged black holes in higher dimensions

International Nuclear Information System (INIS)

Chakrabarti, Sayan K.

2009-01-01

In this work we study the Dirac quasinormal modes of higher dimensional charged black holes. Higher dimensional Reissner-Nordstroem type black holes as well as charged black holes in Einstein-Gauss-Bonnet theories are studied for fermionic perturbations using WKB method. A comparative study of the quasinormal modes in the two different theories of gravity has been performed. The behavior of the frequencies with the variation of black hole parameters as well as with the variation of space-time dimensions is studied. We also study the large multipole number limit of the black hole potential in order to look for an analytic expression for the frequencies. (orig.)

Photoconductivity in Dirac materials

International Nuclear Information System (INIS)

Shao, J. M.; Yang, G. W.

2015-01-01

Two-dimensional (2D) Dirac materials including graphene and the surface of a three-dimensional (3D) topological insulator, and 3D Dirac materials including 3D Dirac semimetal and Weyl semimetal have attracted great attention due to their linear Dirac nodes and exotic properties. Here, we use the Fermi’s golden rule and Boltzmann equation within the relaxation time approximation to study and compare the photoconductivity of Dirac materials under different far- or mid-infrared irradiation. Theoretical results show that the photoconductivity exhibits the anisotropic property under the polarized irradiation, but the anisotropic strength is different between 2D and 3D Dirac materials. The photoconductivity depends strongly on the relaxation time for different scattering mechanism, just like the dark conductivity

Integrating out the Dirac sea

Energy Technology Data Exchange (ETDEWEB)

Karbstein, Felix

2009-07-08

We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''{pi} meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)

Fermions in noncommutative emergent gravity

International Nuclear Information System (INIS)

Klammer, D.

2010-01-01

Noncommutative emergent gravity is a novel framework disclosing how gravity is contained naturally in noncommutative gauge theory formulated as a matrix model. It describes a dynamical space-time which itself is a four-dimensional brane embedded in a higher-dimensional space. In noncommutative emergent gravity, the metric is not a fundamental object of the model; rather it is determined by the Poisson structure and by the induced metric of the embedding. In this work the coupling of fermions to these matrix models is studied from the point of view of noncommutative emergent gravity. The matrix Dirac operator as given by the IKKT matrix model defines an appropriate coupling for fermions to an effective gravitational metric of noncommutative four-dimensional spaces that are embedded into a ten-dimensional ambient space. As it turns out this coupling is non-standard due to a spin connection that vanishes in the preferred but unobservable coordinates defined by the model. The purpose of this work is to study the one-loop effective action of this approach. Standard results of the literature cannot be applied due to this special coupling of the fermions. However, integrating out these fields in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the noncommutative structure to the Riemann tensor, and a dilaton-like term. It remains to be understood what the effects of these terms are and whether they can be avoided. In a second step, the existence of a duality between noncommutative gauge theory and gravity which explains the phenomenon of UV/IR mixing as a gravitational effect is discussed. We show how the gravitational coupling of fermions can be interpreted as a coupling of fermions to gauge fields, which suffers then from UV/IR mixing. This explanation does not render the model finite but it reveals why some UV/IR mixing remains even in supersymmetric models, except in the N

Liouville equation of relativistic charged fermion

International Nuclear Information System (INIS)

Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

1991-01-01

As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

Bosonisation of four dimensional real fermionic string models and asymmetric orbifolds

International Nuclear Information System (INIS)

Bailin, D.; Dunbar, D.C.; Love, A.

1990-01-01

Models of four dimensional strings based on internal world-sheet fermions are bosonised and the partition functions are compared with the partition functions of asymmetric Z 2 M orbifold models. Selection rules and couplings are also compared between the two formations. (orig.)

Higher dimensional supersymmetric quantum mechanics and Dirac ...

Indian Academy of Sciences (India)

We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering `mass' as a function of coordinates. Its usefulness in solving potential problems is discussed with specific examples. We also discuss the `physical' significance of the supersymmetric states in this formalism.

Ambiguities and subtleties in fermion mass terms in practical quantum field theory

International Nuclear Information System (INIS)

Cheng, Yifan; Kong, Otto C.W.

2014-01-01

This is a review on structure of the fermion mass terms in quantum field theory, under the perspective of its practical applications in the real physics of Nature—specifically, we discuss fermion mass structure in the Standard Model of high energy physics, which successfully describes fundamental physics up to the TeV scale. The review is meant to be pedagogical, with detailed mathematics presented beyond the level one can find any easily in the textbooks. The discussions, however, bring up important subtleties and ambiguities about the subject that may be less than well appreciated. In fact, the naive perspective of the nature and masses of fermions as one would easily drawn from the presentations of fermion fields and their equations of motion from a typical textbook on quantum field theory leads to some confusing or even wrong statements which we clarify here. In particular, we illustrate clearly that a Dirac fermion mass eigenstate is mathematically equivalent to two degenerated Majorana fermion mass eigenstates at least as long as the mass terms are concerned. There are further ambiguities and subtleties in the exact description of the eigenstate(s). Especially, for the case of neutrinos, the use of the Dirac or Majorana terminology may be mostly a matter of choice. The common usage of such terminology is rather based on the broken SU(2) charges of the related Weyl spinors hence conventional and may not be unambiguously extended to cover more complicate models. - Highlights: • Structure of fermion mass terms in practical quantum field theory is reviewed. • Important subtleties and ambiguities on the subject are clarified. • A mass eigenstate Dirac fermion and two degenerated Majorana ones are equivalent. • The conventional meaning of such terminology for neutrinos is critically discussed

AEMnSb2 (AE=Sr, Ba): a new class of Dirac materials

International Nuclear Information System (INIS)

Farhan, M Arshad; Lee, Geunsik; Shim, Ji Hoon

2014-01-01

The Dirac fermions of Sb square net in AEMnSb 2 (AE=Sr, Ba) are investigated by using first-principles calculation. BaMnSb 2 contains Sb square net layers with a coincident stacking of Ba atoms, exhibiting Dirac fermion behavior. On the other hand, SrMnSb 2 has a staggered stacking of Sr atoms with distorted zig-zag chains of Sb atoms. Application of hydrostatic pressure on the latter induces a structural change from a staggered to a coincident arrangement of AE ions accompanying a transition from insulator to a metal containing Dirac fermions. The structural investigations show that the stacking type of cation and orthorhombic distortion of Sb layers are the main factors to decide the crystal symmetry of the material. We propose that the Dirac fermions can be obtained by controlling the size of cation and the volume of AEMnSb 2 compounds. (fast track communication)

Dispersive estimates for massive Dirac operators in dimension two

Science.gov (United States)

Erdoğan, M. Burak; Green, William R.; Toprak, Ebru

2018-05-01

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t-1 decay rate holds in the L1 →L∞ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of t-1(log ⁡ t) - 2 is attained for large t, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.

Chiral lattice fermions, minimal doubling, and the axial anomaly

International Nuclear Information System (INIS)

Tiburzi, B. C.

2010-01-01

Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity, we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from nonconservation of the flavor-singlet current. Similar nonconservation also leads to the axial anomaly in the case of the naieve lattice action. For minimally doubled actions, however, fine-tuning of the action and axial current is necessary to arrive at the anomaly. Conservation of the flavor nonsinglet vector current additionally requires the current to be fine-tuned. Finally, we determine that the chiral projection of a minimally doubled fermion action can be used to arrive at a lattice theory with an undoubled Dirac fermion possessing the correct anomaly in the continuum limit.

Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

OpenAIRE

Assili, Mohamed; Haddad, Sonia

2013-01-01

We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase where Dirac points disappear. Based on a universal Hamiltonian proposed to describe the motion and the merging of Dirac points in two dimensional Dirac electron cr...

Relativistic two-body system in (1+1)-dimensional QED. 1. On the circle S1

International Nuclear Information System (INIS)

Barut, A.O.; Saradzhev, F.M.

1994-01-01

From the coupled Maxwell-Dirac equations for two fermion fields Ψ 1 , Ψ 2 the authors derive a covariant two-body equation for the composite field Φ(x 1 , x 2 ) in configuration space which includes radiative self-energy effects. Both Coulomb gauge and covariant gauge have been used and their equivalence is proved. For the space S 1 the authors solve the two-body equation with mutual interactions exactly and obtain the mass spectrum in the case of massless fermions. 7 refs., 5 figs

Some polarization properties of many-fermion systems for N-dimensional worlds in the framework of self-consistent renormalization

International Nuclear Information System (INIS)

Kucheryavy, V.I.

1997-01-01

Using the self-consistent renormalization we calculate five types of quantities (having the mass anisotropy in general) associated with the canonical Ward identities and reduction identities for two-point chronological fermion current correlators which describe most general polarization properties of fermionic sector for all n-dimensional quantum field theories incorporating fermions with both degenerate and nondegenerate fermion mass spectrum. The analysis of the vector and axial-vector Ward identities and the reduction ones for regular values of these quantities is carried out. The effective formulae for nontrivial quantum corrections (NQC) to the canonical Ward identities are obtained for any space-time dimension. The properties of the NQC are investigated in detail. The emphasis on the space-time dimension and the signature dependence has been made. Particular properties of the two-dimensional words are pointed out

Fermion fractionization and index theorem

International Nuclear Information System (INIS)

Hirayama, Minoru; Torii, Tatsuo

1982-01-01

The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)

Quantum oscillation and nontrivial transport in the Dirac semimetal Cd_3As_2 nanodevice

International Nuclear Information System (INIS)

Pan, Haiyang; Wei, Zhongxia; Zhao, Bo; Song, Fengqi; Wang, Baigeng; Zhang, Kang; Gao, Ming; Wang, Xuefeng; Zhang, Rong; Wang, Jue; Han, Min; Pi, Li

2016-01-01

Here, we report on the Shubnikov-de Haas oscillation in high-quality Cd_3As_2 nanowires grown by a chemical vapor deposition approach. The dominant transport of topological Dirac fermions is evident by the nontrivial Berry phase in the Landau Fan diagram. The quantum oscillations rise at a small field of 2 T and preserves up to 100 K, revealing a sizeable Landau level gap and a device mobility of 2138 cm"2" V"−"1" s"−"1. The angle-variable oscillations indicate the isotropy of the bulk Dirac transport. The large estimated mean free path makes the Cd_3As_2 nanowire a promising platform for the one-dimensional transport of Dirac semimetals.

Light-front Ward-Takahashi identity for two-fermion systems

International Nuclear Information System (INIS)

Marinho, J. A. O.; Frederico, T.; Pace, E.; Salme, G.; Sauer, P. U.

2008-01-01

We propose a three-dimensional electromagnetic current operator within light-front dynamics that satisfies a light-front Ward-Takahashi identity for two-fermion systems. The light-front current operator is obtained by a quasipotential reduction of the four-dimensional current operator and acts on the light-front valence component of bound or scattering states. A relation between the light-front valence wave function and the four-dimensional Bethe-Salpeter amplitude both for bound or scattering states is also derived, such that the matrix elements of the four-dimensional current operator can be fully recovered from the corresponding light-front ones. The light-front current operator can be perturbatively calculated through a quasipotential expansion, and the divergence of the proposed current satisfies a Ward-Takahashi identity at any given order of the expansion. In the quasipotential expansion the instantaneous terms of the fermion propagator are accounted for by the effective interaction and two-body currents. We exemplify our theoretical construction in the Yukawa model in the ladder approximation, investigating in detail the current operator at the lowest nontrivial order of the quasipotential expansion of the Bethe-Salpeter equation. The explicit realization of the light-front form of the Ward-Takahashi identity is verified. We also show the relevance of instantaneous terms and of the pair contribution to the two-body current and the Ward-Takahashi identity

On the Hamiltonian formalism of the tetrad-gravity with fermions

Science.gov (United States)

Lagraa, M. H.; Lagraa, M.

2018-06-01

We extend the analysis of the Hamiltonian formalism of the d-dimensional tetrad-connection gravity to the fermionic field by fixing the non-dynamic part of the spatial connection to zero (Lagraa et al. in Class Quantum Gravity 34:115010, 2017). Although the reduced phase space is equipped with complicated Dirac brackets, the first-class constraints which generate the diffeomorphisms and the Lorentz transformations satisfy a closed algebra with structural constants analogous to that of the pure gravity. We also show the existence of a canonical transformation leading to a new reduced phase space equipped with Dirac brackets having a canonical form leading to the same algebra of the first-class constraints.

Role of zero modes in the canonical quantization of heavy-fermion QED in light-cone coordinates

International Nuclear Information System (INIS)

Brown, R.W.; Jun, J.W.; Shvartsman, S.M.; Taylor, C.C.

1993-01-01

Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in the zero-mode and the nonzero-mode sectors separately. In both sectors we obtain the physical variables and their canonical commutation relations. The physical Hamiltonian is constructed via a step-by-step exclusion of the unphysical degrees of freedom. An example using this Hamiltonian in which the zero modes play a role is the verification of the correct Coulomb potential between two heavy fermions

Two applications of Berry's phase in fermionic field theory

International Nuclear Information System (INIS)

Goff, W.E.

1989-01-01

When quantized fermions are coupled to a background field, nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superfluid 3 He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the 3 He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero groundstate Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work

Scanning tunneling spectroscopy of the surface states of Dirac fermions in thermoelectrics based on bismuth telluride

Science.gov (United States)

Lukyanova, L. N.; Makarenko, I. V.; Usov, O. A.; Dementev, P. A.

2018-05-01

The morphology of the interlayer van der Waals surface and differential tunneling conductance in p-Bi2‑xSbxTe3‑ySey solid solutions were studied by scanning tunneling microscopy and spectroscopy in dependence on compositions. The topological characteristics of the Dirac fermion surface states were determined. It was shown that the thermoelectric power factor and the material parameter enhance with the shift of the Dirac point to the top of the valence band with the increasing of atomic substitution in these thermoelectrics. A correlation between topological characteristics, power factor and material parameters was found. A growth contribution of the surface states is determined by an increase of the Fermi velocity for large atomic substitutions of Bi at x > 1.5 and small substitutions in the Te sublattice (y = 0.06). In compositions with smaller substitutions at x = (1–1.3) and y = (0.06–0.09), similar effect of the surface states is determined by raising the surface concentration of charge carriers.

S-wave scattering of fermion revisited

International Nuclear Information System (INIS)

Rahaman, Anisur

2011-01-01

A model where a Dirac fermion is coupled to background dilaton field is considered to study s-wave scattering of fermion by a back ground dilaton black hole. It is found that an uncomfortable situation towards information loss scenario arises when one loop correction gets involved during bosonization.

Thermal radiation of fermions by an accelerated wall

International Nuclear Information System (INIS)

Horibe, Minoru

1979-01-01

The theory of particle production by an accelerated wall is extended to the massless Dirac particle. It is shown that the mean occupation number of fermions (anti-fermions) is given by the Fermi distribution function. (author)

Peccei-Quinn symmetry for Dirac seesaw and leptogenesis

Energy Technology Data Exchange (ETDEWEB)

Gu, Pei-Hong [Department of Physics and Astronomy, Shanghai Jiao Tong University,800 Dongchuan Road, Shanghai 200240 (China)

2016-07-04

We extend the DFSZ invisible axion model to simultaneously explain small Dirac neutrino masses and cosmic matter-antimatter asymmetry. After the Peccei-Quinn and electroweak symmetry breaking, the effective Yukawa couplings of the Dirac neutrinos to the standard model Higgs scalar can be highly suppressed by the ratio of the vacuum expectation value of an iso-triplet Higgs scalar over the masses of some heavy gauge-singlet fermions, iso-doublet Higgs scalars or iso-triplet fermions. The iso-triplet fields can carry a zero or nonzero hypercharge. Through the decays of the heavy gauge-singlet fermions, iso-doublet scalars or iso-triplet fermions, we can obtain a lepton asymmetry in the left-handed leptons and an opposite lepton asymmetry in the right-handed neutrinos. Since the right-handed neutrinos do not participate in the sphaleron processes, the left-handed lepton asymmetry can be partially converted to a baryon asymmetry.

Designing Two-Dimensional Dirac Heterointerfaces of Few-Layer Graphene and Tetradymite-Type Sb2Te3 for Thermoelectric Applications.

Science.gov (United States)

Jang, Woosun; Lee, Jiwoo; In, Chihun; Choi, Hyunyong; Soon, Aloysius

2017-12-06

Despite the ubiquitous nature of the Peltier effect in low-dimensional thermoelectric devices, the influence of finite temperature on the electronic structure and transport in the Dirac heterointerfaces of the few-layer graphene and layered tetradymite, Sb 2 Te 3 (which coincidently have excellent thermoelectric properties) are not well understood. In this work, using the first-principles density-functional theory calculations, we investigate the detailed atomic and electronic structure of these Dirac heterointerfaces of graphene and Sb 2 Te 3 and further re-examine the effect of finite temperature on the electronic band structures using a phenomenological temperature-broadening model based on Fermi-Dirac statistics. We then proceed to understand the underlying charge redistribution process in this Dirac heterointerfaces and through solving the Boltzmann transport equation, we present the theoretical evidence of electron-hole asymmetry in its electrical conductivity as a consequence of this charge redistribution mechanism. We finally propose that the hexagonal-stacked Dirac heterointerfaces are useful as efficient p-n junction building blocks in the next-generation thermoelectric devices where the electron-hole asymmetry promotes the thermoelectric transport by "hot" excited charge carriers.

easyDiracGauginos

International Nuclear Information System (INIS)

Abel, Steven; Goodsell, Mark

2011-02-01

A simple and natural model is presented that gives Dirac gauginos. The configuration is related to ''deconstructed gaugino mediation''. A high energy completion is provided based on existing ISS-like models of deconstructed gaugino mediation. This provides a complete picture of Dirac gauginos that includes the necessary extra adjoint fermions (generated as magnetic quarks of the ISS theory) and supersymmetry breaking (via the ISS mechanism). Moreover the screening of the scalar masses means that they can similar to or less than the gaugino masses, even though the supersymmetry breaking is driven by F-terms. (orig.)

Wigner functions for fermions in strong magnetic fields

Science.gov (United States)

Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

2018-02-01

We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

Running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions

Science.gov (United States)

Bergner, Georg; Piemonte, Stefano

2018-04-01

Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N =1 supersymmetric Yang-Mills (SYM) theory and minimal walking technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N =1 SYM, minimal walking technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to compute the running coupling in the MiniMom scheme. We analyze several different ensembles of lattice Monte Carlo simulations for the SU(2) adjoint QCD with Nf=1 /2 ,1 ,3 /2 , and 2 Dirac fermions. We show how the running of the coupling changes as the number of interacting fermions is increased towards the conformal window.

Axial anomalies of Lifshitz fermions

CERN Document Server

Bakas, Ioannis

2011-01-01

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the eta-invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non-relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Horava-Lifshitz theory and find that the index is non-zero provided that the space-time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2)xU(1) isom...

Asymptotic fermion propagator in massless three-dimensional QED

International Nuclear Information System (INIS)

Hand, B.J.

1993-01-01

Massless quantum electrodynamics in two spatial and one time dimensions has a logarithmically confining static Coulomb potential, and thus nontrivial infrared behavior. We apply a technique developed for ordinary four-dimensional quantum electrodynamics in which the charged asymptotic states in the theory are dressed with soft vector bosons, in order to improve the representation of the infrared dynamics in perturbation theory. The resulting modification to the mass-shell behavior of the fermion propagator is determined, with the result that the propagator no longer possesses a mass-shell singularity

Model space dimensionalities for multiparticle fermion systems

International Nuclear Information System (INIS)

Draayer, J.P.; Valdes, H.T.

1985-01-01

A menu driven program for determining the dimensionalities of fixed-(J) [or (J,T)] model spaces built by distributing identical fermions (electrons, neutrons, protons) or two distinguihable fermion types (neutron-proton and isospin formalisms) among any mixture of positive and negative parity spherical orbitals is presented. The algorithm, built around the elementary difference formula d(J)=d(M=J)-d(M=J+1), takes full advantage of M->-M and particle-hole symmetries. A 96 K version of the program suffices for as compilated a case as d[(+1/2, +3/2, + 5/2, + 7/2-11/2)sup(n-26)J=2 + ,T=7]=210,442,716,722 found in the 0hω valence space of 56 126 Ba 70 . The program calculates the total fixed-(Jsup(π)) or fixed-(Jsup(π),T) dimensionality of a model space generated by distributing a specified number of fermions among a set of input positive and negative parity (π) spherical (j) orbitals. The user is queried at each step to select among various options: 1. formalism - identical particle, neutron-proton, isospin; 2. orbits -bumber, +/-2*J of all orbits; 3. limits -minimum/maximum number of particles of each parity; 4. specifics - number of particles, +/-2*J (total), 2*T; 5. continue - same orbit structure, new case quit. Though designed for nuclear applications (jj-coupling), the program can be used in the atomic case (LS-coupling) so long as half integer spin values (j=l+-1/2) are input for the valnce orbitals. Mutiple occurrences of a given j value are properly taken into account. A minor extension provides labelling information for a generalized seniority classification scheme. The program logic is an adaption of methods used in statistical spectroscopy to evaluate configuration averages. Indeed, the need for fixed symmetry leve densities in spectral distribution theory motivated this work. The methods extend to other group structures where there are M-like additive quantum labels. (orig.)

Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

Energy Technology Data Exchange (ETDEWEB)

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de [Institut für theoretische Physik, Philosophenweg 16, D-69120 Heidelberg (Germany); Noh, Changsuk, E-mail: changsuk@kias.re.kr [Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com [Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 (Singapore); School of Electronic and Computer Engineering, Technical University of Crete, Chania, Crete, 73100 (Greece)

2016-11-15

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.

Renormalization of fermion mixing

International Nuclear Information System (INIS)

Schiopu, R.

2007-01-01

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

Renormalization of fermion mixing

Energy Technology Data Exchange (ETDEWEB)

Schiopu, R.

2007-05-11

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

Double valley Dirac fermions for 3D and 2D Hg$_{1-x}$Cd$_x$Te with strong asymmetry

OpenAIRE

Marchewka, M.

2017-01-01

In this paper the possibility to bring about the double- valley Dirac fermions in some quantum structures is predicted. These quantum structures are: strained 3D Hg$_{1-x}$Cd$_x$Te topological insulator (TI) with strong interface inversion asymmetry and the asymmetric Hg$_{1-x}$Cd$_x$Te double quantum wells (DQW). The numerical analysis of the dispersion relation for 3D TI Hg$_{1-x}$Cd$_x$Te for the proper Cd ($x$)-content of in the Hg$_{1-x}$Cd$_x$Te-compound clearly show that the inversion ...

Particle-like solutions of the Einstein-Dirac-Maxwell equations

Science.gov (United States)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-08-01

We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

Exact solution of the N-dimensional generalized Dirac-Coulomb equation

International Nuclear Information System (INIS)

Tutik, R.S.

1992-01-01

An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)

Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces

International Nuclear Information System (INIS)

Arai, A.

1985-01-01

We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)

easyDiracGauginos

Energy Technology Data Exchange (ETDEWEB)

Abel, Steven [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; CERN, Geneva (Switzerland); Goodsell, Mark [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2011-02-15

A simple and natural model is presented that gives Dirac gauginos. The configuration is related to ''deconstructed gaugino mediation''. A high energy completion is provided based on existing ISS-like models of deconstructed gaugino mediation. This provides a complete picture of Dirac gauginos that includes the necessary extra adjoint fermions (generated as magnetic quarks of the ISS theory) and supersymmetry breaking (via the ISS mechanism). Moreover the screening of the scalar masses means that they can similar to or less than the gaugino masses, even though the supersymmetry breaking is driven by F-terms. (orig.)

Spontaneous symmetry breaking and fermion chirality in higher-dimensional gauge theory

International Nuclear Information System (INIS)

Wetterich, C.

1985-01-01

The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to H=SU(3)sub(C)xSU(2)sub(L)xU(1)sub(R)xU(1)sub(B-L). For all solutions, the fermions which are chiral with respect to H form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)sub(G)xU(1)sub(G). For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)sub(G)xU(1)sub(G). Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories. (orig.)

Confinement limit of a Dirac particle in two and three dimensions

International Nuclear Information System (INIS)

Toyama, F.M.; Nogami, Y.

2010-01-01

Consider a particle that is in a stationary state described by the Dirac equation with a finite-range potential. In two and three dimensions the particle can be confined to an arbitrarily small spatial region. This is in contrast to the one-dimensional case in which the confinement region cannot be much narrower than the Compton wavelength.

On ghost fermions

International Nuclear Information System (INIS)

Grensing, G.

2002-01-01

The path integral for ghost fermions, which is heuristically made use of in the Batalin-Fradkin-Vilkovisky approach to quantization of constrained systems, is derived from first principles. The derivation turns out to be rather different from that of physical fermions since the definition of Dirac states for ghost fermions is subtle. With these results at hand, it is then shown that the nonminimal extension of the Becchi-Rouet-Stora-Tyutin operator must be chosen differently from the notorious choice made in the literature in order to avoid the boundary terms that have always plagued earlier treatments. Furthermore it is pointed out that the elimination of states with nonzero ghost number requires the introduction of a thermodynamic potential for ghosts; the reason is that Schwarz's Lefschetz formula for the partition function of the time-evolution operator is not capable, despite claims to the contrary, to get rid of nonzero ghost number states on its own. Finally, we comment on the problems of global topological nature that one faces in the attempt to obtain the solutions of the Dirac condition for physical states in a configuration space of nontrivial geometry; such complications give rise to anomalies that do not obey the Wess-Zumino consistency conditions. (orig.)

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

Energy Technology Data Exchange (ETDEWEB)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

2015-10-15

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.

A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles

Science.gov (United States)

Finster, Felix

2011-08-01

In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical system by a collection of Dirac states, including the states of the Dirac sea. Formulating the interaction by an action principle for the fermionic projector, we obtain a consistent description of interacting quantum fields which reproduces the results of perturbative quantum field theory. We find a new mechanism for the generation of boson masses and obtain small corrections to the field equations which violate causality.

Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons

Directory of Open Access Journals (Sweden)

Yuichi Otsuka

2016-03-01

Full Text Available The metal-insulator transition has been a subject of intense research since Mott first proposed that the metallic behavior of interacting electrons could turn to an insulating one as electron correlations increase. Here, we consider electrons with massless Dirac-like dispersion in two spatial dimensions, described by the Hubbard models on two geometrically different lattices, and perform numerically exact calculations on unprecedentedly large systems that, combined with a careful finite-size scaling analysis, allow us to explore the quantum critical behavior in the vicinity of the interaction-driven metal-insulator transition. Thereby, we find that the transition is continuous, and we determine the quantum criticality for the corresponding universality class, which is described in the continuous limit by the Gross-Neveu model, a model extensively studied in quantum field theory. Furthermore, we discuss a fluctuation-driven scenario for the metal-insulator transition in the interacting Dirac electrons: The metal-insulator transition is triggered only by the vanishing of the quasiparticle weight, not by the Dirac Fermi velocity, which instead remains finite near the transition. This important feature cannot be captured by a simple mean-field or Gutzwiller-type approximate picture but is rather consistent with the low-energy behavior of the Gross-Neveu model.

Experimental Observation of Three-Component New Fermions in Topological Semimetal MoP

Science.gov (United States)

Lv, B. Q.; Feng, Z.-L.; Xu, Q.-N.; Ma, J.-Z.; Kong, L.-Y.; Richard, Pierre; Huang, Y.-B.; Strocov, V. N.; Fang, C.; Weng, H.-M.; Shi, Y.-G.; Qian, Tian; Ding, Hong; Paul Scherrer Institute, Swiss Light Source, CH-5232 Villigen PSI, Switzerland Team; Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics Team; University of Chinese Academy of Sciences, Beijing 100190, China Team; Collaborative Innovation Center of Quantum Matter, Beijing, China Collaboration; Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Team

Condensed matter systems can host quasiparticle excitations that are analogues to elementary particles such as Majorana, Weyl, and Dirac fermions. Recent advances in band theory have expanded the classification of fermions in crystals, and revealed crystal symmetry-protected electron excitations that have no high-energy counterparts. Here, using angle-resolved photoemission spectroscopy, we demonstrate the existence of a triply degenerate point in the electronic structure of MoP crystal, where the quasiparticle excitations are beyond the Majorana-Weyl-Dirac classification. Furthermore, we observe pairs of Weyl points in the bulk electronic structure coexisting with the new fermions, thus introducing a platform for studying the interplay between different types of fermions. We thank Binbin Fu, Nan Xu, and Xin Gao for the assistance in the ARPES experiments.

Dirac particle on S2

International Nuclear Information System (INIS)

Ferreira, P.L.; Palladino, B.E.

1985-01-01

The problem of a Dirac particle in stationary motion on S 2 - a two dimensional sphere embedded in Euclidean space E 3 - is discussed. It provides a particularly simple case of an exactly solvable constrained Dirac particle whose properties are here studied, with emphasis on its magnetic moment. (Author) [pt

Fermionic cosmologies

International Nuclear Information System (INIS)

Chimento, L P; Forte, M; Devecchi, F P; Kremer, G M; Ribas, M O; Samojeden, L L

2011-01-01

In this work we review if fermionic sources could be responsible for accelerated periods during the evolution of a FRW universe. In a first attempt, besides the fermionic source, a matter constituent would answer for the decelerated periods. The coupled differential equations that emerge from the field equations are integrated numerically. The self-interaction potential of the fermionic field is considered as a function of the scalar and pseudo-scalar invariants. It is shown that the fermionic field could behave like an inflaton field in the early universe, giving place to a transition to a matter dominated (decelerated) period. In a second formulation we turn our attention to analytical results, specifically using the idea of form-invariance transformations. These transformations can be used for obtaining accelerated cosmologies starting with conventional cosmological models. Here we reconsider the scalar field case and extend the discussion to fermionic fields. Finally we investigate the role of a Dirac field in a Brans-Dicke (BD) context. The results show that this source, in combination with the BD scalar, promote a final eternal accelerated era, after a matter dominated period.

Double Dirac cones in phononic crystals

KAUST Repository

Li, Yan

2014-07-07

A double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal (PC) consisting of a triangular array of core-shell-structure cylinders in water. The double Dirac cone is induced by the accidental degeneracy of two double-degenerate Bloch states. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can also be accurately predicted from the method. Because the double Dirac cone occurs at a relatively low frequency, a slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated by two examples. Potential applications can be expected in diverse fields such as acoustic wave manipulations and energy flow control.

Double Dirac cones in phononic crystals

KAUST Repository

Li, Yan; Wu, Ying; Mei, Jun

2014-01-01

A double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal (PC) consisting of a triangular array of core-shell-structure cylinders in water. The double Dirac cone is induced by the accidental degeneracy of two double-degenerate Bloch states. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can also be accurately predicted from the method. Because the double Dirac cone occurs at a relatively low frequency, a slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated by two examples. Potential applications can be expected in diverse fields such as acoustic wave manipulations and energy flow control.

How real are composite fermions?

International Nuclear Information System (INIS)

Kang, W.; Stormer, H.L.; Pfeiffer, L.N.; Baldwin, K.W.; West, K.W.

1995-01-01

A new picture of fractional quantum Hall effect (FQHE) in terms of a novel particle called composite fermion has emerged recently. A composite fermion is a composite of two flux quanta which are effectively bound to an electron as a result of electron-electron interaction. A system of electrons at half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field with a distinct Fermi surface. The FQHE is then viewed as the integral quantum Hall effect of composite fermions away from half-filling. In order to test for these new particles, we have studied transport of anti-dot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the anti-dot lattice. At half-filling we observe the same dimensional resonances. This establishes the ''semi-classical'' behavior of composite fermions. (orig.)

Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

International Nuclear Information System (INIS)

Habib, K. M. Masum; Ghosh, Avik W.; Sajjad, Redwan N.

2016-01-01

Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

Energy Technology Data Exchange (ETDEWEB)

Habib, K. M. Masum, E-mail: masum.habib@virginia.edu; Ghosh, Avik W. [Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904 (United States); Sajjad, Redwan N. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2016-03-14

Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

Wilson Fermions and Axion Electrodynamics in Optical Lattices

International Nuclear Information System (INIS)

Bermudez, A.; Martin-Delgado, M. A.; Mazza, L.; Rizzi, M.; Goldman, N.; Lewenstein, M.

2010-01-01

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.

Heat kernel expansion for fermionic billiards in an external magnetic field

International Nuclear Information System (INIS)

Antoine, M.; Comtet, A.; Knecht, M.

1989-05-01

Using Seeley's heat kernel expansion, we compute the asymptotic density of states of the Dirac operator coupled to a magnetic field on a two dimensional manifold with boundary (fermionic billiard). Local boundary conditions compatible with vector current conservation depend on a free parameter α. It is shown that the perimeter correction identically vanishes for α = 0. In that case, the next order constant term is found to be proportional to the Euler characteristic of the manifold. These results are independent of the external magnetic field and of the shape of the billiard, provided the boundary is sufficiently smooth. For the flat circular billiard, the constant term is found to be - 1/12, in agreement with a numerical result by M.V. BERRY and R.J. MONDRAGON (1987)

Local moment formation in Dirac electrons

International Nuclear Information System (INIS)

Mashkoori, M; Mahyaeh, I; Jafari, S A

2015-01-01

Elemental bismuth and its compounds host strong spin-orbit interaction which is at the heart of topologically non-trivial alloys based on bismuth. These class of materials are described in terms of 4x4 matrices at each v point where spin and orbital labels of the underlying electrons are mixed. In this work we investigate the single impurity Anderson model (SIAM) within a mean field approximation to address the nature of local magnetic moment formation in a generic Dirac Hamiltonian. Despite the spin-mixing in the Hamiltonian, within the Hartree approximation it turns out that the impuritys Green function is diagonal in spin label. In the three dimensional Dirac materials defined over a bandwidth D and spin-orbit parameter γ, that hybridizes with impurity through V, a natural dimensionless parameter V 2 D/2πγ 3 emerges. So neither the hybridization strength, V, nor the spin-orbit coupling γ, but a combination thereof governs the phase diagram. By tuning chemical potential and the impurity level, we present phase diagram for various values of Hubbard U. Numerical results suggest that strong spin-orbit coupling enhances the local moment formation both in terms of its strength and the area of the local moment region. In the case that we tune the chemical potential in a similar way as normal metal we find that magnetic region is confined to μ ≥ ε 0 , in sharp contrast to 2D Dirac fermions. If one fixes the chemical potential and tunes the impurity level, phase diagram has two magnetic regions which corresponds to hybridization of impurity level with lower and upper bands. (paper)

Path-integral bosonization of two-dimensional massive Q.C.D

International Nuclear Information System (INIS)

Rego Monteiro, M.A. do.

1984-01-01

The fermionic determinant for two-dimensional QCD with massive fermions by means of Seeley's technique is evaluated. Apart from a gluon-mass term this determinant contains a Wess-Zumino anomaly term and a non-abelian extension of the Sine-Gordon. (Author) [pt

New symmetries for the Dirac equation

International Nuclear Information System (INIS)

Linhares, C.A.; Mignaco, J.A.

1990-01-01

The Dirac equation in four dimension is studied describing fermions, both as 4 x 4 matrices and differential forms. It is discussed in both formalisms its properties under transformations of the group SU(4). (A.C.A.S.) [pt

Nonequilibrium fermion production in quantum field theory

International Nuclear Information System (INIS)

Pruschke, Jens

2010-01-01

The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio

Nonequilibrium fermion production in quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Pruschke, Jens

2010-06-16

The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio

Nonperturbative volume reduction of large-N QCD with adjoint fermions

International Nuclear Information System (INIS)

Bringoltz, Barak; Sharpe, Stephen R.

2009-01-01

We use nonperturbative lattice techniques to study the volume-reduced 'Eguchi-Kawai' version of four-dimensional large-N QCD with a single adjoint Dirac fermion. We explore the phase diagram of this single-site theory in the space of quark mass and gauge coupling using Wilson fermions for a number of colors in the range 8≤N≤15. Our evidence suggests that these values of N are large enough to determine the nature of the phase diagram for N→∞. We identify the region in the parameter space where the (Z N ) 4 center symmetry is intact. According to previous theoretical work using the orbifolding paradigm, and assuming that translation invariance is not spontaneously broken in the infinite-volume theory, in this region volume reduction holds: the single-site and infinite-volume theories become equivalent when N→∞. We find strong evidence that this region includes both light and heavy quarks (with masses that are at the cutoff scale), and our results are consistent with this region extending toward the continuum limit. We also compare the action density and the eigenvalue density of the overlap Dirac operator in the fundamental representation with those obtained in large-N pure-gauge theory.

Construction of two-dimensional quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Klimek, S.; Kondracki, W.

1987-12-01

We present a sketch of the construction of the functional measure for the SU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.

Hamiltonian formulation and BRS quantization of the fermionic string in the covariant gauge

International Nuclear Information System (INIS)

Kim, J.; Koh, I.G.; Song, D.

1988-01-01

The canonical formalism for fermion string theory is constructed in a covariant way following Dirac's prescription. The second-class constraints between fermionic fields and their conjugate momenta require the Dirac brackets. The algebra of the constraints is found, which is reduced to the superconformal algebra at an orthonormal gauge. Through the Batalin, Fradkin, and Vilkovisky method of the Becchi-Rouet-Stora- (BRS-) invariant formalism, the (classical) BRS charge and the generating functional are obtained

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

DEFF Research Database (Denmark)

Loft, Niels Jakob; Salami Dehkharghani, Amin; Mehta, N. P.

2015-01-01

We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in t...

Pseudoclassical fermionic model and classical solutions

International Nuclear Information System (INIS)

Smailagic, A.

1981-08-01

We study classical limit of fermionic fields seen as Grassmann variables and deduce the proper quantization prescription using Dirac's method for constrained systems and investigate quantum meaning of classical solutions for the Thirring model. (author)

The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

International Nuclear Information System (INIS)

Finster, Felix; Grotz, Andreas

2010-01-01

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

Science.gov (United States)

Finster, Felix; Grotz, Andreas

2010-07-01

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

Band nesting, massive Dirac fermions, and valley Landé and Zeeman effects in transition metal dichalcogenides: A tight-binding model

Science.gov (United States)

Bieniek, Maciej; Korkusiński, Marek; Szulakowska, Ludmiła; Potasz, Paweł; Ozfidan, Isil; Hawrylak, Paweł

2018-02-01

We present here the minimal tight-binding model for a single layer of transition metal dichalcogenides (TMDCs) MX 2(M , metal; X , chalcogen) which illuminates the physics and captures band nesting, massive Dirac fermions, and valley Landé and Zeeman magnetic field effects. TMDCs share the hexagonal lattice with graphene but their electronic bands require much more complex atomic orbitals. Using symmetry arguments, a minimal basis consisting of three metal d orbitals and three chalcogen dimer p orbitals is constructed. The tunneling matrix elements between nearest-neighbor metal and chalcogen orbitals are explicitly derived at K ,-K , and Γ points of the Brillouin zone. The nearest-neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective 6 ×6 Hamiltonian giving correct composition of metal and chalcogen orbitals but not the direct gap at K points. The direct gap at K , correct masses, and conduction band minima at Q points responsible for band nesting are obtained by inclusion of next-neighbor Mo-Mo tunneling. The parameters of the next-nearest-neighbor model are successfully fitted to MX 2(M =Mo ; X =S ) density functional ab initio calculations of the highest valence and lowest conduction band dispersion along K -Γ line in the Brillouin zone. The effective two-band massive Dirac Hamiltonian for MoS2, Landé g factors, and valley Zeeman splitting are obtained.

Fermi Surface with Dirac Fermions in CaFeAsF Determined via Quantum Oscillation Measurements

Science.gov (United States)

Terashima, Taichi; Hirose, Hishiro T.; Graf, David; Ma, Yonghui; Mu, Gang; Hu, Tao; Suzuki, Katsuhiro; Uji, Shinya; Ikeda, Hiroaki

2018-02-01

Despite the fact that 1111-type iron arsenides hold the record transition temperature of iron-based superconductors, their electronic structures have not been studied much because of the lack of high-quality single crystals. In this study, we comprehensively determine the Fermi surface in the antiferromagnetic state of CaFeAsF, a 1111 iron-arsenide parent compound, by performing quantum oscillation measurements and band-structure calculations. The determined Fermi surface consists of a symmetry-related pair of Dirac electron cylinders and a normal hole cylinder. From analyses of quantum-oscillation phases, we demonstrate that the electron cylinders carry a nontrivial Berry phase π . The carrier density is of the order of 10-3 per Fe. This unusual metallic state with the extremely small carrier density is a consequence of the previously discussed topological feature of the band structure which prevents the antiferromagnetic gap from being a full gap. We also report a nearly linear-in-B magnetoresistance and an anomalous resistivity increase above about 30 T for B ∥c , the latter of which is likely related to the quantum limit of the electron orbit. Intriguingly, the electrical resistivity exhibits a nonmetallic temperature dependence in the paramagnetic tetragonal phase (T >118 K ), which may suggest an incoherent state. Our study provides a detailed knowledge of the Fermi surface in the antiferromagnetic state of 1111 parent compounds and moreover opens up a new possibility to explore Dirac-fermion physics in those compounds.

Fermi Surface with Dirac Fermions in CaFeAsF Determined via Quantum Oscillation Measurements

Directory of Open Access Journals (Sweden)

Taichi Terashima

2018-02-01

Full Text Available Despite the fact that 1111-type iron arsenides hold the record transition temperature of iron-based superconductors, their electronic structures have not been studied much because of the lack of high-quality single crystals. In this study, we comprehensively determine the Fermi surface in the antiferromagnetic state of CaFeAsF, a 1111 iron-arsenide parent compound, by performing quantum oscillation measurements and band-structure calculations. The determined Fermi surface consists of a symmetry-related pair of Dirac electron cylinders and a normal hole cylinder. From analyses of quantum-oscillation phases, we demonstrate that the electron cylinders carry a nontrivial Berry phase π. The carrier density is of the order of 10^{-3} per Fe. This unusual metallic state with the extremely small carrier density is a consequence of the previously discussed topological feature of the band structure which prevents the antiferromagnetic gap from being a full gap. We also report a nearly linear-in-B magnetoresistance and an anomalous resistivity increase above about 30 T for B∥c, the latter of which is likely related to the quantum limit of the electron orbit. Intriguingly, the electrical resistivity exhibits a nonmetallic temperature dependence in the paramagnetic tetragonal phase (T>118  K, which may suggest an incoherent state. Our study provides a detailed knowledge of the Fermi surface in the antiferromagnetic state of 1111 parent compounds and moreover opens up a new possibility to explore Dirac-fermion physics in those compounds.

Cut-off parameters in the one-dimensional two-fermion model

International Nuclear Information System (INIS)

Apostol, M.

1982-07-01

It is shown that the usual cut-off procedure (α cut-off parameter) employed in the boson representation of the fermion field opepators of the one-djmensional two-fermion model (TFM) is an incorrect one as the computator of the hermitean-conjugate field operators at the same space-point fails to fulfil a certain relationship which was pointed out long ago by Jordan. The complete form of the boson representation (including the zero-mode) of a single fermion field and the correct values of the cut-off parameter α is reviewed following Jordan and generalized to the TFM. The cut-off parameter α corresponds to a bandwidth cut-off and Jordan's boson representation is exact only in the limit α → 0. The additional zero-mode terms make the exact solution of the backscattering and umklapp scattering problem to be valid only if a supplementary condition is imposed on the coupling constants. Using the present bosonization technique all the inconsistencies of the TFM are removed. The one-particle Green's function and response functions of the Tomonaga-Luttinger model (TLM) are calculated and found to be identical with those obtained by direct diagram summation. The energy gap appearing in the spectrum of the TFM with backscattering and umklapp scattering for certain values of the coupling constants is shown to be proportional to the momentum transfer cut-off γ -1 which has to be kept finite while α goes to zero. Under such conditions the anticommunication relations and Jordan's commutator are invariant under the canonical transformation on the boson operators that diagonalizes the Hamiltonian of the TLM. The charge-density response function of the TFM with backscattering is perturbationally calculated up to the first order. The cut-off α -1 applies in the same way to terms which differ only by their spin indices in the expression of this response function. The charge-density response function is also evaluated at low frequencies for the exactly soluble TFM with

Large anomalous magnetic moment in three-dimensional Dirac and Weyl semimetals

NARCIS (Netherlands)

Van Der Wurff, E. C I; Stoof, H. T C

2016-01-01

We investigate the effect of Coulomb interactions on the electromagnetic response of three-dimensional Dirac and Weyl semimetals. In a calculation reminiscent of Schwinger's seminal work on quantum electrodynamics, we find three physically distinct effects for the anomalous magnetic moment of the

On the trace anomaly of a Weyl fermion

Energy Technology Data Exchange (ETDEWEB)

Bastianelli, Fiorenzo; Martelli, Riccardo [Dipartimento di Fisica e Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy)

2016-11-29

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa’s method supplemented by a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.

Worldline path integrals for fermions with general couplings

International Nuclear Information System (INIS)

D'Hoker, E.; Gagne, D.G.

1996-01-01

We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance. (orig.)

On charged fermions in two dimensions

International Nuclear Information System (INIS)

Randjbar-Daemi, S.; Salam, A.; Strathdee, J.

1990-09-01

The integer quantum Hall effect and associated magnetic phenomena are reconsidered in a 2-dimensional system with a flat boundary. The electromagnetic properties of this system are governed by an effective Lagrangian which includes an induced Chern-Simons term. The effective lagrangian is relevant for the description of fields which are slowly varying about a uniform magnetic background associated with a fermionic ground state in which a whole number of Landau levels is filled. It is singular for field values that correspond to partially filled levels. The underlying assumption of translation invariance of the fermionic ground state fails in the vicinity of boundaries where the effective field theory is essentially non-local. The width of the boundary layer and the current flowing in it are estimated. (author). 12 refs, 5 figs

Pressure induced superconductivity in the antiferromagnetic Dirac material BaMnBi2.

Science.gov (United States)

Chen, Huimin; Li, Lin; Zhu, Qinqing; Yang, Jinhu; Chen, Bin; Mao, Qianhui; Du, Jianhua; Wang, Hangdong; Fang, Minghu

2017-05-09

The so-called Dirac materials such as graphene and topological insulators are a new class of matter different from conventional metals and (doped) semiconductors. Superconductivity induced by doing or applying pressure in these systems may be unconventional, or host mysterious Majorana fermions. Here, we report a successfully observation of pressure-induced superconductivity in an antiferromagnetic Dirac material BaMnBi 2 with T c of ~4 K at 2.6 GPa. Both the higher upper critical field, μ 0 H c2 (0) ~ 7 Tesla, and the measured current independent of T c precludes that superconductivity is ascribed to the Bi impurity. The similarity in ρ ab (B) linear behavior at high magnetic fields measured at 2 K both at ambient pressure (non-superconductivity) and 2.6 GPa (superconductivity, but at the normal state), as well as the smooth and similar change of resistivity with pressure measured at 7 K and 300 K in zero field, suggests that there may be no structure transition occurred below 2.6 GPa, and superconductivity observed here may emerge in the same phase with Dirac fermions. Our findings imply that BaMnBi 2 may provide another platform for studying SC mechanism in the system with Dirac fermions.

Bragg diffraction of fermions at optical potentials

International Nuclear Information System (INIS)

Deh, Benjamin

2008-01-01

This thesis describes the Bragg diffraction of ultracold fermions at an optical potential. A moving optical lattice was created, by overlaying two slightly detuned lasers. Atoms can be diffracted at this lattice if the detuning fulfills the Bragg condition for resting atoms. This Bragg diffraction is analyzed systematically in this thesis. To this end Rabi oscillations between the diffraction states were driven, as well in the weakly interacting Bragg regime, as in the strongly interacting Kapitza-Dirac regime. Simulations, based on a driven two-, respectively multilevel-system describe the observed effects rather well. Furthermore, the temporal evolution of the diffracted states in the magnetic trapping potential was studied. The anharmonicity of the trap in use and the scattering cross section for p-wave collisions in a 6 Li system was determined from the movement of these states. Moreover the momentum distribution of the fermions was measured with Bragg spectroscopy and first signs of Fermi degeneracy were found. Finally an interferometer with fermions was build, exhibiting a coherence time of more than 100 μs. With this, the possibility for measurement and manipulation of ultracold fermions with Bragg diffraction could bee shown. (orig.)

Distribution for fermionic discrete lattice gas within the canonical ensemble

International Nuclear Information System (INIS)

Kutner, R.; Barszczak, T.

1991-01-01

The distinct deviations from the Fermi-Dirac statistics ascertained recently at low temperatures for a one-dimensional, spinless fermionic discrete lattice gas with conserved number of noninteracting particles hopping on the nondegenerated, well-separated single-particle energy levels are studied in numerical and theoretical terms. The generalized distribution is derived in the form n(h) = {Y h exp[(var-epsilon h -μ)β]+1} -1 valid even in the thermodynamic limit, when the discreteness of the energy levels is kept. This distribution demonstrates good agreement with the data obtained numerically both by the canonical partition-function technique and by Monte Carlo simulation

The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave

Science.gov (United States)

Finster, Felix; Reintjes, Moritz

2017-05-01

We give a non-perturbative construction of a distinguished state for the quantized Dirac field in Minkowski space in the presence of a time-dependent external field of the form of a plane electromagnetic wave. By explicit computation of the fermionic signature operator, it is shown that the Dirac operator has the strong mass oscillation property. We prove that the resulting fermionic projector state is a Hadamard state.

Dirac Material Graphene

OpenAIRE

Sheka, Elena F.

2016-01-01

The paper presents the author view on spin-rooted properties of graphene supported by numerous experimental and calculation evidences. Dirac fermions of crystalline graphene and local spins of graphene molecules are suggested to meet a strict demand - different orbitals for different spins- which leads to a large spectrum of effects caused by spin polarization of electronic states. The consequent topological non-triviality, making graphene topological insulator, and local spins, imaging graph...

Signatures from an extra-dimensional seesaw model

International Nuclear Information System (INIS)

Blennow, Mattias; Melbeus, Henrik; Ohlsson, Tommy; Zhang He

2010-01-01

We study the generation of small neutrino masses in an extra-dimensional model, where singlet fermions are allowed to propagate in the extra dimension, while the standard model particles are confined to a brane. Motivated by the fact that extra-dimensional models are nonrenormalizable, we truncate the Kaluza-Klein towers at a maximal Kaluza-Klein number. This truncation, together with the structure of the bulk Majorana mass term, motivated by the Sherk-Schwarz mechanism, implies that the Kaluza-Klein modes of the singlet fermions pair to form Dirac fermions, except for a number of unpaired Majorana fermions at the top of each tower. These heavy Majorana fermions are the only sources of lepton number breaking in the model, and similarly to the type-I seesaw mechanism, they naturally generate small masses for the left-handed neutrinos. The lower Kaluza-Klein modes mix with the light neutrinos, and the mixing effects are not suppressed with respect to the light-neutrino masses. Compared to conventional fermionic seesaw models, such mixing can be more significant. We study the signals of this model at the Large Hadron Collider, and find that the current low-energy bounds on the nonunitarity of the leptonic mixing matrix are strong enough to exclude an observation.

Weak antilocalization in a three-dimensional topological insulator based on a high-mobility HgTe film

Science.gov (United States)

Savchenko, M. L.; Kozlov, D. A.; Kvon, Z. D.; Mikhailov, N. N.; Dvoretsky, S. A.

2016-09-01

The anomalous magnetoresistance (AMR) caused by the weak antilocalization effects in a three-dimensional topological insulator based on a strained mercury telluride film is experimentally studied. It is demonstrated that the obtained results are in a good agreement with the universal theory of Zduniak, Dyakonov, and Knap. It is found that the AMR in the bulk band gap is far below that expected for the system of Dirac fermions. Such a discrepancy can assumingly be related to a nonzero effective mass of Dirac fermions. The filling of energy bands in the bulk is accompanied by a pronounced increase in the AMR. This is a signature of the weak coupling between the surface and bulk charge carriers.

Spectral density and a family of Dirac operators

International Nuclear Information System (INIS)

Niemi, A.J.

1985-01-01

The spectral density for a class Dirac operators is investigated by relating its even and odd parts to the Riemann zeta-function and to the eta-invariant by Atiyah, Padoti and Singer. Asymptotic expansions are studied and a 'hidden' supersymmetry is revealed and used to relate the Dirac operator to a supersymmetric quantum mechanics. A general method for the computation of the odd spectral density is developed, and various applications are discussed. In particular the connection to the fermion number and a relation between the odd spectral density and some ratios of Jost functions and relative phase shifts are pointed out. Chiral symmetry breaking is investigated using methods analogous to those applied in the investigation of the fermion number, and related to supersymmetry breaking in the corresponding quantum mechanical model. (orig.)

Four-fermi anomalous dimension with adjoint fermions

CERN Document Server

Del Debbio, Luigi; Ruano, Carlos Pena

2014-01-01

The four-fermi interaction can play an important role in models of strong dynamical EW sym- metry breaking if the anomalous dimensions of the four-fermi operators become large in the IR. We discuss a number of issues that are relevant for the nonperturbative computation of the four- fermi anomalous dimensions for the SU(2) gauge theory with two flavors of Dirac fermions in the adjoint representation, using a Schrödinger functional formalism.

Dark matter scenarios in a constrained model with Dirac gauginos

CERN Document Server

Goodsell, Mark D.; Müller, Tobias; Porod, Werner; Staub, Florian

2015-01-01

We perform the first analysis of Dark Matter scenarios in a constrained model with Dirac Gauginos. The model under investigation is the Constrained Minimal Dirac Gaugino Supersymmetric Standard model (CMDGSSM) where the Majorana mass terms of gauginos vanish. However, $R$-symmetry is broken in the Higgs sector by an explicit and/or effective $B_\\mu$-term. This causes a mass splitting between Dirac states in the fermion sector and the neutralinos, which provide the dark matter candidate, become pseudo-Dirac states. We discuss two scenarios: the universal case with all scalar masses unified at the GUT scale, and the case with non-universal Higgs soft-terms. We identify different regions in the parameter space which fullfil all constraints from the dark matter abundance, the limits from SUSY and direct dark matter searches and the Higgs mass. Most of these points can be tested with the next generation of direct dark matter detection experiments.

Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Science.gov (United States)

Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.

2018-01-01

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons

Directory of Open Access Journals (Sweden)

Eckart Marsch

2015-04-01

Full Text Available We revisit the charge-conjugation operation for the Dirac equation in its chiral representation. A new decomposition of the Dirac spinor field is suggested and achieved by means of projection operators based on charge conjugation, which is discussed here in a non-standard way. Thus, two separate two-component Majorana-type field equations for the eigenfields of the charge-conjugation operator are obtained. The corresponding free fields are entirely separated without a gauge field, but remain mixed and coupled together through an electromagnetic field term. For fermions that are charged and, thus, subjected to the gauge field of electrodynamics, these two Majorana fields can be reassembled into a doublet, which is equivalent to a standard four-component Dirac spinor field. In this way, the Dirac equation is retained in a new guise, which is fully equivalent to that equation in its chiral form.

Functional approach without path integrals to finite temperature free fermions

International Nuclear Information System (INIS)

Souza, S.M. de; Santos, O. Rojas; Thomaz, M.T.

1999-01-01

Charret et al applied the properties of Grassmann generators to develop a new method to calculate the coefficients of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d ≥1). The methodology explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. we apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the β-independent and μindependent infinities that plague the continuum path integral formulation. (author)

Quantum corrections to ward identities of chronological AVV- and AAA-current correlators for nondegenerate many-fermion systems in the four-dimensional world

International Nuclear Information System (INIS)

Kucheryavij, V.Yi.

1994-01-01

The explicit form of nontrivial quantum corrections to Ward identities for AVV- and AAA-current correlators in the four-dimensional world for nondegenerate many-fermion systems of general type is obtained. The characteristics of all nontrivial quantum corrections for nondegenerate two-flavour fermion systems are classified and described. In particular, the well-known results follow from ours for the trivial quantum corrections (anomalies) in the case of the degenerate spectrum of fermion masses

Lorentz Invariance Violation and Modified Hawking Fermions Tunneling Radiation

Directory of Open Access Journals (Sweden)

Shu-Zheng Yang

2016-01-01

Full Text Available Recently the modified Dirac equation with Lorentz invariance violation has been proposed, which would be helpful to resolve some issues in quantum gravity theory and high energy physics. In this paper, the modified Dirac equation has been generalized in curved spacetime, and then fermion tunneling of black holes is researched under this correctional Dirac field theory. We also use semiclassical approximation method to get correctional Hamilton-Jacobi equation, so that the correctional Hawking temperature and correctional black hole’s entropy are derived.

Real-Time Dynamics in the (1+1)-D Abelian Higgs Model with Fermions

NARCIS (Netherlands)

Aarts, G.; Smit, J.

2000-01-01

In approximate dynamical equations, inhomogenous classical (mean) gauge and Higgs fields are coupled to quantized fermions. The equations are solved numerically on a spacetime lattice. The fermions appear to equilibrate according to the Fermi-Dirac distribution with time-dependent temperature and

High-temperature expansion of the one-loop effective action induced by scalar and Dirac particles

Energy Technology Data Exchange (ETDEWEB)

Kalinichenko, Igor; Kazinski, Peter [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)

2017-12-15

The complete nonperturbative expressions for the high-temperature expansion of the one-loop effective action induced by the charged scalar and the charged Dirac particles both at zero and finite temperatures are derived with account of possible nontrivial boundary conditions. The background electromagnetic field is assumed to be stationary and such that the corresponding Klein-Gordon operator or the Dirac Hamiltonian is self-adjoint. The contributions of particles and antiparticles are obtained separately. The explicit expressions for the C-symmetric and the non-C-symmetric vacuum energies of the Dirac fermions are derived. The leading corrections to the high-temperature expansion due to the nontrivial boundary conditions are explicitly found. The corrections to the logarithmic divergence of the effective action that come from the boundary conditions are derived. The high-temperature expansion of the naive one-loop effective action induced by charged fermions turns out to be divergent in the limit of a zero fermion mass. (orig.)

The spectrum of a Dirac-like operator class and the topology in two dimensions

International Nuclear Information System (INIS)

Botelho, Luiz C.L.

1998-05-01

It is shown, in a relatively simple way and based on Seeley pseudo-differential operator theory, that the main result of Atiyah-Singer in which the trace of the evolution operator associated to a Dirac-like operator class defined in two-dimensional manifolds and coming out of Quantum Physics has a deep topological meaning

Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension

Science.gov (United States)

Roy, Bitan; Foster, Matthew S.

2018-01-01

We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal and a symmetry-preserving band insulator. The electronic dispersion at this critical point is anisotropic (Ek=±√{v2kx2+b2ky2 n } with n =2 ), which results in unconventional scaling of thermodynamic and transport quantities. Because of the vanishing density of states [ϱ (E )˜|E |1 /n ], this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions, the direct Dirac-semimetal to band-insulator transition can either (i) become a fluctuation-driven first-order transition (although unlikely in a particular microscopic model considered here, the anisotropic honeycomb lattice extended Hubbard model) or (ii) get avoided by an intervening broken-symmetry phase. We perform a controlled renormalization group analysis with the small parameter ɛ =1 /n , augmented with a 1 /n expansion (parametrically suppressing quantum fluctuations in the higher dimension) by perturbing away from the one-dimensional limit, realized by setting ɛ =0 and n →∞ . We identify charge density wave (CDW), antiferromagnet (AFM), and singlet s -wave superconductivity as the three dominant candidates for broken symmetry. The onset of any such order at strong coupling (˜ɛ ) takes place through a continuous quantum phase transition across an interacting multicritical point, where the ordered phase, band insulator, Dirac, and anisotropic semimetals meet. We also present the phase diagram of an extended Hubbard model for the ASM, obtained via the controlled deformation of its counterpart in one dimension. The latter displays spin-charge separation and instabilities to CDW, spin density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The spin density wave and Luther-Emery liquid phases deform into pseudospin SU(2)-symmetric quantum critical points separating the

Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension

Directory of Open Access Journals (Sweden)

Bitan Roy

2018-03-01

Full Text Available We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal and a symmetry-preserving band insulator. The electronic dispersion at this critical point is anisotropic (E_{k}=±sqrt[v^{2}k_{x}^{2}+b^{2}k_{y}^{2n}] with n=2, which results in unconventional scaling of thermodynamic and transport quantities. Because of the vanishing density of states [ϱ(E∼|E|^{1/n}], this anisotropic semimetal (ASM is stable against weak short-range interactions. However, for stronger interactions, the direct Dirac-semimetal to band-insulator transition can either (i become a fluctuation-driven first-order transition (although unlikely in a particular microscopic model considered here, the anisotropic honeycomb lattice extended Hubbard model or (ii get avoided by an intervening broken-symmetry phase. We perform a controlled renormalization group analysis with the small parameter ε=1/n, augmented with a 1/n expansion (parametrically suppressing quantum fluctuations in the higher dimension by perturbing away from the one-dimensional limit, realized by setting ε=0 and n→∞. We identify charge density wave (CDW, antiferromagnet (AFM, and singlet s-wave superconductivity as the three dominant candidates for broken symmetry. The onset of any such order at strong coupling (∼ε takes place through a continuous quantum phase transition across an interacting multicritical point, where the ordered phase, band insulator, Dirac, and anisotropic semimetals meet. We also present the phase diagram of an extended Hubbard model for the ASM, obtained via the controlled deformation of its counterpart in one dimension. The latter displays spin-charge separation and instabilities to CDW, spin density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The spin density wave and Luther-Emery liquid phases deform into pseudospin SU(2-symmetric quantum critical

Spin-excited oscillations in two-component fermion condensates

International Nuclear Information System (INIS)

Maruyama, Tomoyuki; Bertsch, George F.

2006-01-01

We investigate collective spin excitations in two-component fermion condensates with special consideration of unequal populations of the two components. The frequencies of monopole and dipole modes are calculated using Thomas-Fermi theory and the scaling approximation. As the fermion-fermion coupling is varied, the system shows various phases of the spin configuration. We demonstrate that spin oscillations have more sensitivity to the spin phase structures than the density oscillations

A Novel Optoelectronic Device Based on Correlated Two-Dimensional Fermions

Science.gov (United States)

Dianat, Pouya

Conventional metallic contacts can be replicated by quantum two dimensional charge (of Fermion) systems (2DFS). Unlike metals, the particle concentration of these "unconventional" systems can be accurately controlled in an extensive range and by means of external electronic or optical stimuli. A 2DFS can, hence, transition from a high-density kinetic liquid into a dilute-but highly correlated-gas state, in which inter-particle Coulombic interactions are significant. Such interactions contribute negatively, by so-called exchange-correlation energies, to the overall energetics of the system, and are manifested as a series negative quantum capacitance. This dissertation investigates the capacitive performance of a class of unconventional devices based on a planar metal-semiconductor-metal structure with an embedded 2DFS. They constitute an opto-electronically controlled variable capacitor, with record breaking figures-of-merit in capacitance tuning ranges of up to 7000 and voltage sensitivities as large as 400. Internal eld manipulations by localized depletion of a dense 2DFS account for the enlarged maximum and reduced minimum capacitances. The capacitance-voltage characteristics of these devices incur an anomalous "Batman" shape capacitance enhancement (CE) of up to 200% that may be triggered optically. The CE is attributed to the release and storage of exchange-correlation energies; from the "unconventional" plate and in the dielectric, respectively. This process is enforced by density manipulation of the 2DFS by a hybrid of an external eld and light-generated carriers. Under moderate optical powers, the capacitance becomes 43 times greater than the dark value; thus a new capacitance-based photodetection method is offered. This new capacitance based photodetection method has a range of applications in optoelectronics, particularly in the next generation of photonic integrated systems.

Hawking radiation of Dirac particles from the Myers-Perry black hole

International Nuclear Information System (INIS)

Mao, Pu-Jian; Jia, Lin-Yu; Li, Ran; Ren, Ji-Rong

2011-01-01

In this paper, we apply the quantum anomaly cancelation method and the effective action approach as well as the method of Damour-Ruffini-Sannan to derive Hawking radiation of Dirac particles from the Myers-Perry black hole. Using the dimensional reduction technique, we find that the fermionic field in the background of the Myers-Perry black hole can be treated as an infinite collection of quantum fields in (1+1)-dimensional background coupled with the dilaton field and the U(1) gauge field near the horizon. Thus Hawking temperature and fluxes are found. The Hawking temperature obtained agrees with the surface gravity formula while the Hawking fluxes derived from the anomaly cancelation method and the effective action approach are in complete agreement with the ones obtained from integrating the Planck distribution. (orig.)

The Role of Zero-Modes in the Canonical Quantization of Heavy-Fermion QED in Light-Cone Coordinates

OpenAIRE

Brown, Robert W.; Jun, Jin Woo; Shvartsman, Shmaryu M.; Taylor, Cyrus C.

1993-01-01

Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti-)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in {the }zero-mode {and the non-zero-mode} sectors separately. In both sectors we obtain the physical variables and their canonical commutation ...

Spectroscopy of Dipolar Fermions in Layered Two-Dimensional and Three-Dimensional Lattices

Science.gov (United States)

2011-09-06

Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the...and study Cooper pair binding [7,8], polaron quasiparticle residue [9], and pseudogap behavior of ultracold fermions across the BEC/BCS crossover [10...imaginary part of this energy is the quasiparticle lifetime, and the only source of quasiparticle decay is the p-wave particle loss. Thus the cloud

Fractional fermions

International Nuclear Information System (INIS)

Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1984-01-01

The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)

Geometry of non-degenerate Susskind fermions

International Nuclear Information System (INIS)

Mitra, P.

1983-01-01

The Dirac-Kaehler equation on the lattice is known to describe the degenerate ''flavours'' appering in Susskind's approach to lattice fermions. We study the modification that has to be made in this equation in order to lift the degeneracy and give the flavours arbitrary different masses. (orig.)

Fermions, Skyrmions and the 3-sphere

International Nuclear Information System (INIS)

Goatham, Stephen W; Krusch, Steffen

2010-01-01

This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalized angular momentum or grand spin. It can be solved explicitly for a Skyrme configuration given by the hedgehog form. The energy spectrum and degeneracies are derived for all values of the grand spin. Solutions for non-zero grand spin are each characterized by a set of four polynomials. The paper also discusses the energy of the Dirac sea using zeta-function regularization.

Graphene – A Two-Dimensional Dirac Material

OpenAIRE

Liu, Danny; Wicklund, Johan

2014-01-01

Graphene is a two-dimensional material, whose popularity has soared in both condensedmatter physics and material science the past decade. Due to its unique properties, graphene can be used in a vast array of new and interesting applications that could fundamentally change the material industry. This report reviews the current research and literature in order to trace the historical development of graphene. Then, in order to better understand the material, the unique properties of graphene are...

Superconducting proximity in three-dimensional Dirac materials: Odd-frequency, pseudoscalar, pseudovector, and tensor-valued superconducting orders

Science.gov (United States)

Faraei, Zahra; Jafari, S. A.

2017-10-01

We find that a conventional s -wave superconductor in proximity to a three-dimensional Dirac material (3DDM), to all orders of perturbation in tunneling, induces a combination of s - and p -wave pairing only. We show that the Lorentz invariance of the superconducting pairing prevents the formation of Cooper pairs with higher orbital angular momenta in the 3DDM. This no-go theorem acquires stronger form when the probability of tunneling from the conventional superconductor to positive and negative energy states of 3DDM are equal. In this case, all the p -wave contribution except for the lowest order, identically vanish and hence we obtain an exact result for the induced p -wave superconductivity in 3DDM. Fierz decomposing the superconducting matrix we find that the temporal component of the vector superconducting order and the spatial components of the pseudovector order have odd-frequency pairing symmetry. We find that the latter is odd with respect to exchange of position and chirality of the electrons in the Cooper pair and is a spin-triplet, which is necessary for NMR detection of such an exotic pseudovector pairing. Moreover, we show that the tensorial order breaks into a polar vector and an axial vector and both of them have conventional pairing symmetry except for being a spin triplet. According to our study, for gapless 3DDM, the tensorial superconducting order will be the only order that is odd with respect to the chemical potential μ . Therefore we predict that a transverse p -n junction binds Majorana fermions. This effect can be used to control the neutral Majorana fermions with electric fields.

Bosonic Analogue of Dirac Composite Fermi Liquid

Science.gov (United States)

Mross, David; Alicea, Jason; Motrunich, Olexei

The status of particle-hole symmetry has long posed a challenge to the theory of the quantum Hall effect. It is expected to be present in the half-filled Landau level, but is absent in the conventional field theory, i.e., the composite Fermi liquid. Recently, Son proposed an alternative, explicitly particle-hole symmetric theory which features composite fermions that exhibit a Dirac dispersion. In my talk, I will introduce an analogous particle-hole-symmetric metallic state of bosons at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2 Ï Berry flux, protected by particle-hole and discrete rotation symmetries. As in the Dirac composite Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the familiar Chern-Simons theory. I will discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as its signatures in experiments and simulations.

Fermion fields in η-ξ spacetime

International Nuclear Information System (INIS)

Gui, Y.

1992-01-01

Fermion fields in η-ζ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in η-ζ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in η-ζ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in η-ζ spacetime originates from Lorentz transformation properties of the fields

Singlet fermionic dark matter with Veltman conditions

OpenAIRE

Kim, Yeong Gyun; Lee, Kang Young; Nam, Soo-hyeon

2018-01-01

We reexamine a renormalizable model of a fermionic dark matter with a gauge singlet Dirac fermion and a real singlet scalar which can ameliorate the scalar mass hierarchy problem of the Standard Model (SM). Our model setup is the minimal extension of the SM for which a realistic dark matter (DM) candidate is provided and the cancellation of one-loop quadratic divergence to the scalar masses can be achieved by the Veltman condition (VC) simultaneously. This model extension, although renormaliz...

Dirac equation in low dimensions: The factorization method

Energy Technology Data Exchange (ETDEWEB)

Sánchez-Monroy, J.A., E-mail: antosan@if.usp.br [Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP (Brazil); Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, Bogotá, D. C. (Colombia); CIF, Bogotá (Colombia)

2014-11-15

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.

Electronic structure of a graphene superlattice with massive Dirac fermions

International Nuclear Information System (INIS)

Lima, Jonas R. F.

2015-01-01

We study the electronic and transport properties of a graphene-based superlattice theoretically by using an effective Dirac equation. The superlattice consists of a periodic potential applied on a single-layer graphene deposited on a substrate that opens an energy gap of 2Δ in its electronic structure. We find that extra Dirac points appear in the electronic band structure under certain conditions, so it is possible to close the gap between the conduction and valence minibands. We show that the energy gap E g can be tuned in the range 0 ≤ E g  ≤ 2Δ by changing the periodic potential. We analyze the low energy electronic structure around the contact points and find that the effective Fermi velocity in very anisotropic and depends on the energy gap. We show that the extra Dirac points obtained here behave differently compared to previously studied systems

Delocalization of Relativistic Dirac Particles in Disordered One-Dimensional Systems and Its Implementation with Cold Atoms

International Nuclear Information System (INIS)

Zhu Shiliang; Zhang Danwei; Wang, Z. D.

2009-01-01

We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to delocalization in comparison with the nonrelativistic particles with the same disorder strength. More intriguingly, we reveal that the massless Dirac particles are entirely delocalized for any energy due to the inherent chiral symmetry, leading to a well-known result that particles are always localized in one-dimensional systems for arbitrary weak disorders to break down. Furthermore, we propose a feasible scheme to detect the delocalization feature of the Dirac particles with cold atoms in a light-induced gauge field.

Collective Interference of Composite Two-Fermion Bosons

DEFF Research Database (Denmark)

Tichy, Malte; Bouvrie, Peter Alexander; Mølmer, Klaus

2012-01-01

The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us...... to provide the full Hong–Ou–Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson....

The hidden fermions in Z(2) theories

International Nuclear Information System (INIS)

Srednicki, M.

1983-01-01

Low dimensional Z(2) gauge theories have been rewritten in terms of locally coupled fermionic degrees of freedom by means of the Jordan-Wigner transformation. In this paper it is shown that higher dimensional Z(2) gauge theories are also fermionic theories in disguise. The SML solution to the 1+1 dimension Ising model is reviewed. Psi operators are represented pictorially as arrows, psi 1 points to the left, psi 2 to the right, each site of H a multiple of two operators. The 2+1 dimension Ising model is then considered. A fermion plaquette operator is introduced as the generator of a gauge symmetry for the fermionic H. Findings in 1+1 and 2+1 are then applied to 3+1 dimensional Z(2) gauge theory. A construction of this lattice is undertaken. Psi formalism replaces sigma formalism, as it permits extremely simple duality transformations to be made on any Z(2) Hamiltonian. It is shown that the fermionic formalism will lead to new ideas in Z(2) theories

(2 + 1)-Dimensional Dirac hierarchy and its integrable couplings as well as multi-component integrable system

International Nuclear Information System (INIS)

Li Zhu; Dong Huanhe

2008-01-01

Under the frame of the (2 + 1)-dimensional zero curvature equation and Tu model, (2 + 1)-dimensional Dirac hierarchy is obtained. Again by use of the expanding loop algebra the integrable coupling system of the above hierarchy is given

Evolution kernel for the Dirac field

International Nuclear Information System (INIS)

Baaquie, B.E.

1982-06-01

The evolution kernel for the free Dirac field is calculated using the Wilson lattice fermions. We discuss the difficulties due to which this calculation has not been previously performed in the continuum theory. The continuum limit is taken, and the complete energy eigenfunctions as well as the propagator are then evaluated in a new manner using the kernel. (author)

Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

International Nuclear Information System (INIS)

Assili, M; Haddad, S

2013-01-01

We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT) 2 I 3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed. (paper)

Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

Science.gov (United States)

Assili, M.; Haddad, S.

2013-09-01

We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.

Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones.

Science.gov (United States)

Assili, M; Haddad, S

2013-09-11

We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.

Fermionic bound states in distinct kinklike backgrounds

Energy Technology Data Exchange (ETDEWEB)

Bazeia, D. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Mohammadi, A. [Universidade Federal de Campina Grande, Departamento de Fisica, Caixa Postal 10071, Campina Grande, Paraiba (Brazil)

2017-04-15

This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have a similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and we consider two distinct boson-fermion interactions, one motivated by supersymmetry and the other described by the standard Yukawa coupling. (orig.)

Highly imbalanced fermion-fermion mixtures in one dimension

International Nuclear Information System (INIS)

Recher, Christian

2013-01-01

interpretation as effective interaction energy for the two minority Fermions in the presence of the Fermi-sea. The second part is devoted to the study of one-dimensional systems consisting of two fermionic particle species with different masses. We show that for specific kinds of interaction potentials and for certain relations between the masses and the coupling constants, the particle creation and annihilation operators of such a system can be constructed exactly.

Analysis of D Dimensional Dirac equation for q -deformed Posch-Teller combined with q -deformed trigonometric Manning Rosen Non-Central potential using Asymptotic Iteration Method (AIM)

International Nuclear Information System (INIS)

Alam, Y.; Suparmi; Cari; Anwar, F.

2016-01-01

In this study, we used asymptotic iteration method (AIM) to obtain the relativistic energy spectra and wavefunctions for D Dimensional Dirac equation. Solution of the D Dimensional Dirac equation using asymptotic iteration method was done by four steps. The first step, we substitutied q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential into D dimensional Dirac equation. And then, general term of D dimensioanl Dirac equation for q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential was reduced into one dimensioanal Dirac equation, consist of radial part and angular part. The second step, both of one dimensional part must be reduced to hypergeometric type differential equation by suitable parameter change. And then, hypergeometric type differential equation was transformed into AIM type differential equation. For the last step, AIM type differential equation can be solved to obtain the relativistic energy and wavefunctions of Dirac equation. Relativistic energy and wavefunctions were visualized by using Matlab software. (paper)

Composite fermions in the quantum Hall effect

International Nuclear Information System (INIS)

Johnson, B.L.; Kirczenow, G.

1997-01-01

The quantum Hall effect and associated quantum transport phenomena in low-dimensional systems have been the focus of much attention for more than a decade. Recent theoretical development of interesting quasiparticles - 'composite fermions' - has led to significant advances in understanding and predicting the behaviour of two-dimensional electron systems under high transverse magnetic fields. Composite fermions may be viewed as fermions carrying attached (fictitious) magnetic flux. Here we review models of the integer and fractional quantum Hall effects, including the development of a unified picture of the integer and fractional effects based upon composite fermions. The composite fermion picture predicts remarkable new physics: the formation of a Fermi surface at high magnetic fields, and anomalous ballistic transport, thermopower, and surface acoustic wave behaviour. The specific theoretical predictions of the model, as well as the body of experimental evidence for these phenomena are reviewed. We also review recent edge-state models for magnetotransport in low-dimensional devices based on the composite fermion picture. These models explain the fractional quantum Hall effect and transport phenomena in nanoscale devices in a unified framework that also includes edge state models of the integer quantum Hall effect. The features of the composite fermion edge-state model are compared and contrasted with those of other recent edge-state models of the fractional quantum Hall effect. (author)

Monopole-fermion and dyon-fermion bound states. Pt. 5

International Nuclear Information System (INIS)

Osland, P.; Harvard Univ., Cambridge, MA; Schultz, C.L.; Wu, T.T.

1985-02-01

We present explicit, approximate, remarkably precise results for the Kazama-Yang hamiltonian, which describes a Dirac monopole interacting with a spin-1/2 fermion that has an extra magnetic moment. The results are valid for bound states of angular momentum j >= Zvertical strokeegvertical stroke+1/2, where the radial wave functions are determined by four coupled differential equations. These equations have been solved analytically for M - E << M, which is a limit of considerable practical interest. Binding energies and wave functions are given. (orig.)

Relativistic quantum Darwinism in Dirac fermion and graphene systems

Science.gov (United States)

Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis

2012-02-01

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.

Path-integral formulation of chiral invariant fermion models in two dimensions

International Nuclear Information System (INIS)

Furuya, K.; Gamboa Saravi, R.E.; Schaposnik, F.A.

1982-01-01

We study the Thirring and chiral-invariant Gross-Neveu (CGN) models using the functional integral method. By introducing an auxiliary vector field we disclose a relation with two-dimensional gauge theories coupled to fermions and then extend a technique based on a chiral change in the functional variables to study purely fermionic models. We obtain the exact Klaiber solution for the massless Thirring model (for spin 1/2) in a very simple way and we then extend our technique to investigate the CGN model. We show the factorization of a free fermionic part at the level of Green functions on very general grounds. We then impose certain restrictions on the behavior of the fields - which render our treatment exact only in the zero winding number sector, but allow the computation of the U(1) part of the CGN Green functions exactly, showing, in particular, its complete decoupling from the color part and the almost long-range order behavior in the infrared region. In our approach, the non-triviality of the jacobian arising from the chiral transformation - directly related to the topological density and the axial anomaly - appears to be crucial for the functional integral treatment of these models. (orig.)

Exact pairing correlations in one-dimensional trapped fermions with stochastic mean-field wave-functions

Energy Technology Data Exchange (ETDEWEB)

Juillet, O.; Gulminelli, F. [Caen Univ., Lab. de Physique Corpusculaire (LPC/ENSICAEN), 14 (France); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)

2003-11-01

The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudo-potential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For an harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated. (author)

Matter fields near quantum critical point in (2+1)-dimensional U(1) gauge theory

International Nuclear Information System (INIS)

Liu Guozhu; Li Wei; Cheng Geng

2010-01-01

We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, r=0, defines a quantum critical point between the Higgs phase and the Coulomb phase. We consider only the critical point r=0 and the Coulomb phase with r>0. The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value N f c , which depends quantitatively on the flavor N b and the scalar boson mass r. When N f f c , the matter fields carrying internal gauge charge are all confined if r≠0 but are deconfined at the quantum critical point r=0. The system has distinct low-energy elementary excitations at the critical point r=0 and in the Coulomb phase with r≠0. We calculate the specific heat and susceptibility of the system at r=0 and r≠0, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.

Fermions on the electroweak string

CERN Document Server

Moreno, J M; Quirós, Mariano; Moreno, J M; Oaknin, D H; Quiros, M

1995-01-01

We construct a simple class of exact solutions of the electroweak theory including the naked Z--string and fermion fields. It consists in the Z--string configuration (\\phi,Z_\\theta), the {\\it time} and z components of the neutral gauge bosons (Z_{0,3},A_{0,3}) and a fermion condensate (lepton or quark) zero mode. The Z--string is not altered (no feed back from the rest of fields on the Z--string) while fermion condensates are zero modes of the Dirac equation in the presence of the Z--string background (no feed back from the {\\it time} and z components of the neutral gauge bosons on the fermion fields). For the case of the n--vortex Z--string the number of zero modes found for charged leptons and quarks is (according to previous results by Jackiw and Rossi) equal to |n|, while for (massless) neutrinos is |n|-1. The presence of fermion fields in its core make the obtained configuration a superconducting string, but their presence (as well as that of Z_{0,3},A_{0,3}) does not enhance the stability of the Z--stri...

The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime

International Nuclear Information System (INIS)

Sierra, Germán

2014-01-01

We construct a Hamiltonian H R whose discrete spectrum contains, in a certain limit, the Riemann zeros. H R is derived from the action of a massless Dirac fermion living in a domain of Rindler spacetime, in 1 + 1 dimensions, which has a boundary given by the world line of a uniformly accelerated observer. The action contains a sum of delta function potentials that can be viewed as partially reflecting moving mirrors. An appropriate choice of the accelerations of the mirrors, provide primitive periodic orbits that are associated with the prime numbers p, whose periods, as measured by the observer's clock, are logp. Acting on the chiral components of the fermion χ ∓ , H R becomes the Berry–Keating Hamiltonian ±(x p-hat + p-hat x)/2, where x is identified with the Rindler spatial coordinate and p-hat with the conjugate momentum. The delta function potentials give the matching conditions of the fermion wave functions on both sides of the mirrors. There is also a phase shift e iϑ for the reflection of the fermions at the boundary where the observer sits. The eigenvalue problem is solved by transfer matrix methods in the limit where the reflection amplitudes become infinitesimally small. We find that, for generic values of ϑ, the spectrum is a continuum where the Riemann zeros are missing, as in the adelic Connes model. However, for some values of ϑ, related to the phase of the zeta function, the Riemann zeros appear as discrete eigenvalues that are immersed in the continuum. We generalize this result to the zeros of Dirichlet L-functions, which are associated to primitive characters, that are encoded in the reflection coefficients of the mirrors. Finally, we show that the Hamiltonian associated to the Riemann zeros belongs to class AIII, or chiral GUE, of the Random Matrix Theory. (paper)

Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions

Energy Technology Data Exchange (ETDEWEB)

Gao, Jian-hua [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, Shandong University, Weihai, Shandong 264209 (China); Wang, Qun, E-mail: qunwang@ustc.edu.cn [Interdisciplinary Center for Theoretical Study and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States)

2015-10-07

We demonstrate the emergence of the magnetic moment and spin-vorticity coupling of chiral fermions in 4-dimensional Wigner functions. In linear response theory with space–time varying electromagnetic fields, the parity-odd part of the electric conductivity can also be derived which reproduces results of the one-loop and the hard-thermal or hard-dense loop. All these properties show that the 4-dimensional Wigner functions capture comprehensive aspects of physics for chiral fermions in electromagnetic fields.

Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

Science.gov (United States)

Li, Shuai; Wang, Chen; Zheng, Shi-Han; Wang, Rui-Qiang; Li, Jun; Yang, Mou

2018-04-01

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.

Strain engineering of Dirac cones in graphyne

Energy Technology Data Exchange (ETDEWEB)

Wang, Gaoxue; Kumar, Ashok; Pandey, Ravindra, E-mail: pandey@mtu.edu [Department of Physics, Michigan Technological University, Houghton, Michigan 49931 (United States); Si, Mingsu [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China)

2014-05-26

6,6,12-graphyne, one of the two-dimensional carbon allotropes with the rectangular lattice structure, has two kinds of non-equivalent anisotropic Dirac cones in the first Brillouin zone. We show that Dirac cones can be tuned independently by the uniaxial compressive strain applied to graphyne, which induces n-type and p-type self-doping effect, by shifting the energy of the Dirac cones in the opposite directions. On the other hand, application of the tensile strain results into a transition from gapless to finite gap system for the monolayer. For the AB-stacked bilayer, the results predict tunability of Dirac-cones by in-plane strains as well as the strain applied perpendicular to the plane. The group velocities of the Dirac cones show enhancement in the resistance anisotropy for bilayer relative to the case of monolayer. Such tunable and direction-dependent electronic properties predicted for 6,6,12-graphyne make it to be competitive for the next-generation electronic devices at nanoscale.

Boson-fermion mass splittings in four-dimensional heterotic string models with anomalous U(1) gauge groups

International Nuclear Information System (INIS)

Yamaguchi, Masahiro; Yamamoto, Hisashi; Onogi, Tetsuya

1989-01-01

In four-dimensional heterotic string models with anomalous U(1) gauge groups, space-time supersymmetry (SUSY) breaks down spontaneously at one loop. In this paper, the Ward-Takahashi identity of broken SUSY in one-loop two-point amplitudes is investigated in all generalities. The boson-fermion mass splitting of any supersymmetric pair in an arbitrary model is proportional to the product of the D-term expectation value (the sum of (chirality)x(U(1) charge) of massless fermions in the model) and the U(1) charge of the external particle. In order to give a better understanding of the results, we present some examples of the mass splittings in a simple Z 3 orbifold model. (orig.)

The principle of the Fermionic projector

CERN Document Server

Finster, Felix

2006-01-01

The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionic projector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective...

Some spectral properties of the one-dimensional disordered Dirac equation

International Nuclear Information System (INIS)

Bocquet, Marc

1999-01-01

We study spectral properties of a one-dimensional Dirac equation with various disorder. We use replicas to calculate the exact density of state and typical localization length of a Dirac particle in several cases. We show that they can be calculated, in quite a simple fashion, in any type of disorder obeying a Gaussian white noise distribution. In addition to cases involving pure types of disorder, we study a mixed disorder case where the Dyson singularity is destroyed by the mixing. We also clarify the supersymmetric alternative derivation, even though it proves less efficient than the replica treatment for such thermodynamic quantities. We show that the smallest dynamical algebra in the Hamiltonian formalism is u(1,1), preferably to u(n,n) in the replica derivation or u(1, 1 vertical bar 2) in the supersymmetric alternative. Finally, we discuss symmetries in the disorder fields and show that there exists a non-trivial mapping between the electric potential disorder and the magnetic (or mass) disorder

Bogoliubov transformations and fermion condensates in lattice field theories

International Nuclear Information System (INIS)

Caracciolo, Sergio; Palumbo, Fabrizio; Viola, Giovanni

2009-01-01

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

Science.gov (United States)

Hyart, T.; Ojajärvi, R.; Heikkilä, T. T.

2018-04-01

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

Collective phenomena in a quasi-two-dimensional system of fermionic polar molecules: Band renormalization and excitons

International Nuclear Information System (INIS)

Babadi, Mehrtash; Demler, Eugene

2011-01-01

We theoretically analyze a quasi-two-dimensional system of fermionic polar molecules trapped in a harmonic transverse confining potential. The renormalized energy bands are calculated by solving the Hartree-Fock equation numerically for various trap and dipolar interaction strengths. The intersubband excitations of the system are studied in the conserving time-dependent Hartree-Fock (TDHF) approximation from the perspective of lattice modulation spectroscopy experiments. We find that the excitation spectrum consists of both intersubband particle-hole excitation continua and antibound excitons whose antibinding behavior is associated to the anisotropic nature of dipolar interactions. The excitonic modes are shown to capture the majority of the spectral weight. We evaluate the intersubband transition rates in order to investigate the nature of the excitonic modes and find that they are antibound states formed from particle-hole excitations arising from several subbands. We discuss the sum rules in the context of lattice modulation spectroscopy experiments and utilize them to check the consistency of the obtained results. Our results indicate that the excitonic effects persist for interaction strengths and temperatures accessible in the current experiments with polar molecules.

Spectral probes of the holographic Fermi ground state: Dialing between the electron star and AdS Dirac hair

International Nuclear Information System (INIS)

Cubrovic, Mihailo; Liu Yan; Schalm, Koenraad; Sun Yawen; Zaanen, Jan

2011-01-01

We argue that the electron star and the anti-de Sitter (AdS) Dirac hair solution are two limits of the free charged Fermi gas in AdS. Spectral functions of holographic duals to probe fermions in the background of electron stars have a free parameter that quantifies the number of constituent fermions that make up the charge and energy density characterizing the electron star solution. The strict electron star limit takes this number to be infinite. The Dirac hair solution is the limit where this number is unity. This is evident in the behavior of the distribution of holographically dual Fermi surfaces. As we decrease the number of constituents in a fixed electron star background the number of Fermi surfaces also decreases. An improved holographic Fermi ground state should be a configuration that shares the qualitative properties of both limits.

Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions

Directory of Open Access Journals (Sweden)

Jian-hua Gao

2015-10-01

Full Text Available We demonstrate the emergence of the magnetic moment and spin-vorticity coupling of chiral fermions in 4-dimensional Wigner functions. In linear response theory with space–time varying electromagnetic fields, the parity-odd part of the electric conductivity can also be derived which reproduces results of the one-loop and the hard-thermal or hard-dense loop. All these properties show that the 4-dimensional Wigner functions capture comprehensive aspects of physics for chiral fermions in electromagnetic fields.

The spectrum of a Dirac-like operator class and the topology in two dimensions; O espectro de uma classe de operadores Dirac e a topologia em 2 dimensoes

Energy Technology Data Exchange (ETDEWEB)

Botelho, Luiz C.L

1998-05-01

It is shown, in a relatively simple way and based on Seeley pseudo-differential operator theory, that the main result of Atiyah-Singer in which the trace of the evolution operator associated to a Dirac-like operator class defined in two-dimensional manifolds and coming out of Quantum Physics has a deep topological meaning 5 refs.

SU(N ) fermions in a one-dimensional harmonic trap

Science.gov (United States)

Laird, E. K.; Shi, Z.-Y.; Parish, M. M.; Levinsen, J.

2017-09-01

We conduct a theoretical study of SU (N ) fermions confined by a one-dimensional harmonic potential. First, we introduce a numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU (N ) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz—derived for a Heisenberg SU(2) spin chain—is extendable to these N -component systems. Lastly, we consider balanced SU (N ) Fermi gases that have an equal number of particles in each spin state for N =2 ,3 ,4 . In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N -component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

Energy Technology Data Exchange (ETDEWEB)

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com [Physics Department, Faculty of Mathematics and Science, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan Surakarta 57126 (Indonesia); Deta, U. A. [Physics Department, Faculty of Science and Mathematics Education and Teacher Training, Surabaya State University, Surabaya (Indonesia)

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

Dirac electronics states in graphene systems: optical spectroscopy studies

Czech Academy of Sciences Publication Activity Database

Orlita, Milan; Potemski, M.

2010-01-01

Roč. 25, č. 6 (2010), 063001/1-063001/22 ISSN 0268-1242 R&D Projects: GA AV ČR KAN400100652 Institutional research plan: CEZ:AV0Z10100521 Keywords : graphene * Dirac fermions Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.323, year: 2010

Dirac and Weyl semimetals with holographic interactions

NARCIS (Netherlands)

Jacobs, V.P.J.

2015-01-01

Dirac and Weyl semimetals are states of matter exhibiting the relativistic physics of, respectively, the Dirac and Weyl equation in a three-dimensional bulk material. These three-dimensional semimetals have recently been realized experimentally in various crystals. Theoretically, especially the

Nucleon form factors with NF=2 twisted mass fermions

International Nuclear Information System (INIS)

Alexandrou, C.; Korzec, T.; Brinet, M.; Carbonell, J.; Harraud, P.A.; Jansen, K.

2009-10-01

We present results on the electromagnetic and axial nucleon form factors using two degenerate flavors of twisted mass fermions on lattices of spatial size 2.1 fm and 2.7 fm and a lattice spacing of about 0.09 fm. We consider pion masses in the range of 260-470MeV.We chirally extrapolate results on the nucleon axial charge, the isovector Dirac and Pauli root mean squared radii and magnetic moment to the physical point and compare to experiment. (orig.)

Scattering of the Dirac particle by a Coulomb plus scalar potential in two dimensions

International Nuclear Information System (INIS)

Dong Shihai; Lozada-Cassou, M.

2004-01-01

The scattering of the two-dimensional Dirac particle by the Coulomb potential Vc=-A1/r plus the scalar one Vs=-A2/r is studied. The phase shifts are obtained exactly. The special case A1=A2 is also discussed. We find that a very interesting feature of the cross section σ(θ) for the special case A1=A2 is symmetrical with respect to the scattering angle θ=π

Look-ahead fermion algorithm

International Nuclear Information System (INIS)

Grady, M.

1986-01-01

I describe a fast fermion algorithm which utilizes pseudofermion fields but appears to have little or no systematic error. Test simulations on two-dimensional gauge theories are described. A possible justification for the algorithm being exact is discussed. 8 refs

Magnetic and Electrical Transport Properties of Dirac Compound BaMnSb2*

Science.gov (United States)

Huang, Silu; Kim, Jisun; Shelton, William. A.; Plummer, Ward; Jin, Rongying

BaMnSb2 is a layered compound containing Sb square nets that is theoretically predicted to host Dirac fermions. We have carried out experimental investigations on electrical transport and magnetic properties of BaMnSb2 single crystals. Both in-plane (ρab) and c-axis (ρc) resistivities show metallic behavior with a small bump in ρc located near 40 K, while there is large anisotropy ρc / ρab ( 100 at 300 K) that increases with decreasing temperature to 1500 at 2 K. Interestingly, Shubnikov-de Hass (SdH) oscillations are observed for both ρab and ρc over a wide temperature and magnetic field range. Quantitative analysis indicates that large amplitude SdH oscillations result from nearly massless Dirac Fermions. Furthermore, our magnetic measurements indicate an A-type antiferromagnetic magnetic ordering below 286 K where ferromagnetic ordering is observed in the ab plane with antiferromagnetic coupling along the c direction. These results indicate that BaMnSb2 is a 2D magnetic Dirac material. This work is supported by NSF through Grant Number DMR-1504226.

Borophane: Stable Two-dimensional Anisotropic Dirac Material with Ultrahigh Fermi Velocity

OpenAIRE

Xu, Lichun; Du, Aijun; Kou, Liangzhi

2016-01-01

Recent synthesis of monolayer borophene (triangle boron monolayer) on the substrate opens the era of boron nanosheet (Science, 350, 1513, $\\mathbf{2015}$), but the structural stability and novel physical properties are still open issues. Here we demonstrated borophene can be stabilized with fully surface hydrogenation, called as borophane, from first-principles calculations. Most interesting, it shows that borophane has direction-dependent Dirac cones, which are mainly contributed by in-plane...

Mass anomalous dimension and running of the coupling in SU(2) with six fundamental fermions

DEFF Research Database (Denmark)

Bursa, Francis; Del Debbio, Luigi; Keegan, Liam

2010-01-01

We simulate SU(2) gauge theory with six massless fundamental Dirac fermions. By using the Schr\\"odinger Functional method we measure the running of the coupling and the fermion mass over a wide range of length scales. We observe very slow running of the coupling and construct an estimator for the...

The Dirac equation in the Lobachevsky space-time

International Nuclear Information System (INIS)

Paramonov, D.V.; Paramonova, N.N.; Shavokhina, N.S.

2000-01-01

The product of the Lobachevsky space and the time axis is termed the Lobachevsky space-time. The Lobachevsky space is considered as a hyperboloid's sheet in the four-dimensional pseudo-Euclidean space. The Dirac-Fock-Ivanenko equation is reduced to the Dirac equation in two special forms by passing from Lame basis in the Lobachevsky space to the Cartesian basis in the enveloping pseudo-Euclidean space

Gauge structure, anomalies and mass generation in a three dimensional thirring model

International Nuclear Information System (INIS)

Gomes, M.; Mendes, R.S.; Ribeiro, R.F.; Silva, A.J. da.

1990-05-01

We consider a three dimensional model of spinor fields with a Thirring like, quadrilinear self interaction. Using either two or four component Dirac spinors, we prove that the 1/N expansion for the model is renormalizable if a gauge structure to select physical quantities is introduced. For certain values of the coupling the leading 1/N approximation exihibits bound state poles. Dynamical breaking of parity or chiral symmetry is shown to occur as a cooperative effect of different orders of 1/N, if N is smaller than the critical value N c = 128 / x 2 D' , where D is two or four depending on wether the fermion field has two or four components. (author) [pt

Generating {mu} and B{mu} in models with Dirac gauginos

Energy Technology Data Exchange (ETDEWEB)

Benakli, Karim [CNRS, UPMC Univ. Paris 06 (France). Lab. de Physique Theorique et Hautes Energies; Goodsell, Mark D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maier, Ann-Kathrin [SB-EPFL, Lausanne (Switzerland). Laboratoire de Physique de la Matiere Complexe

2011-04-15

We consider the extension of the Minimal Supersymmetric Standard Model by Dirac masses for the gauginos. We study the possibility that the same singlet S that pairs up with the bino, to form a Dirac fermion, is used to generate {mu} and B{mu} terms through its vacuum expectation value. For this purpose, we assume that, in the Higgs potential, the necessary R-symmetry breaking originates entirely from a superpotential term ({kappa})/(3)S{sup 3} and discuss the implications for the spectrum of the model. (orig.)

Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Gonzalez, P.A. [Facultad de Ingenieria y Ciencias, Universidad Diego Portales, Santiago (Chile); Vasquez, Yerko; Villalobos, Ruth Noemi [Universidad de La Serena, Departamento de Fisica y Astronomia, Facultad de Ciencias, La Serena (Chile)

2017-09-15

We study the propagation of massless fermionic fields in the background of a three-dimensional Lifshitz black hole, which is a solution of conformal gravity. The black-hole solution is characterized by a vanishing dynamical exponent. Then we compute analytically the quasinormal modes, the area spectrum, and the absorption cross section for fermionic fields. The analysis of the quasinormal modes shows that the fermionic perturbations are stable in this background. The area and entropy spectrum are evenly spaced. In the low frequency limit, it is observed that there is a range of values of the angular momentum of the mode that contributes to the absorption cross section, whereas it vanishes in the high frequency limit. In addition, by a suitable change of variables a gravitational soliton can also be obtained and the stability of the quasinormal modes are studied and ensured. (orig.)

Q-deformed Grassmann field and the two-dimensional Ising model

International Nuclear Information System (INIS)

Bugrij, A.I.; Shadura, V.N.

1994-01-01

In this paper we construct the exact representation of the Ising partition function in form of the SL q (2,R)-invariant functional integral for the lattice free q-fermion field theory (q=-1). It is shown that the proposed method of q-fermionization allows one to re-express the partition function of the eight vertex model in external field through the functional integral with four-fermion interaction. For the construction of these representation we define a lattice (l,q,s)-deformed Grassmann bi spinor field and extend the Berezin integration rules for this field. At q = - 1, l = s 1 we obtain the lattice q-fermion field which allows to fermionize the two-dimensional Ising model. We show that Gaussian integral over (q,s)-Grassmann variables is expressed through the (q,s)-deformed Pfaffian which is equal to square root of the determinant of some matrix at q = ± 1, s = ±1. (author). 39 refs

On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

Science.gov (United States)

Hulko, Artem

2018-03-01

In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.

Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

Institute of Scientific and Technical Information of China (English)

LI Ning; JU Guo-Xing; REN Zhong-Zhou

2004-01-01

The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The twodimensional Dirac oscillator has similar behavior to that for three-dimensional one.

Long-lived trimers in a quasi-two-dimensional Fermi system

Science.gov (United States)

Laird, Emma K.; Kirk, Thomas; Parish, Meera M.; Levinsen, Jesper

2018-04-01

We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold 6Li atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the 6Li system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.

The emergence of geometry: a two-dimensional toy model

CERN Document Server

Alfaro, Jorge; Puigdomenech, Daniel

2010-01-01

We review the similarities between the effective chiral lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zwei-bein is generated from a topological theory without any pre-existing metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several non-standard features this simple toy model appears to be renormalizable and at long distances is described by an effective lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared re...

Two-dimensional Lorentz-Weyl anomaly and gravitational Chern-Simons theory

International Nuclear Information System (INIS)

Chamseddine, A.H.; Froehlich, J.

1992-01-01

Two-dimensional chiral fermions and bosons, more generally conformal blocks of two-dimensional conformal field theories, exhibit Weyl-, Lorentz- and mixed Lorentz-Weyl anomalies. A novel way of computing these anomalies for a system of chiral bosons of arbitrary conformal spin j is sketched. It is shown that the Lorentz- and mixed Lorentz-Weyl anomalies of these theories can be cancelled by the anomalies of a three-dimensional classical Chern-Simons action for the spin connection, expressed in terms of the dreibein field. Some tentative applications of this result to string theory are indicated. (orig.)

Majorana fermion codes

International Nuclear Information System (INIS)

Bravyi, Sergey; Terhal, Barbara M; Leemhuis, Bernhard

2010-01-01

We initiate the study of Majorana fermion codes (MFCs). These codes can be viewed as extensions of Kitaev's one-dimensional (1D) model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of MFCs is to protect quantum information against low-weight fermionic errors, that is, operators acting on sufficiently small subsets of fermionic modes. We examine to what extent MFCs can surpass qubit stabilizer codes in terms of their stability properties. A general construction of 2D MFCs is proposed that combines topological protection based on a macroscopic code distance with protection based on fermionic parity conservation. Finally, we use MFCs to show how to transform any qubit stabilizer code to a weakly self-dual CSS code.

Full utilization of semi-Dirac cones in photonics

Science.gov (United States)

Yasa, Utku G.; Turduev, Mirbek; Giden, Ibrahim H.; Kurt, Hamza

2018-05-01

In this study, realization and applications of anisotropic zero-refractive-index materials are proposed by exposing the unit cells of photonic crystals that exhibit Dirac-like cone dispersion to rotational symmetry reduction. Accidental degeneracy of two Bloch modes in the Brillouin zone center of two-dimensional C2-symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed C2-symmetric photonic crystals behave as epsilon-and-mu-near-zero materials (ɛeff≈ 0 , μeff≈ 0 ) along one propagation direction, but behave as epsilon-near-zero material (ɛeff≈ 0 , μeff≠ 0 ) for the perpendicular direction at semi-Dirac frequency. By extracting the effective medium parameters of the proposed C4- and C2-symmetric periodic media that exhibit Dirac-like and semi-Dirac cone dispersions, intrinsic differences between isotropic and anisotropic materials are investigated. Furthermore, advantages of utilizing semi-Dirac cone materials instead of Dirac-like cone materials in photonic applications are demonstrated in both frequency and time domains. By using anisotropic transmission behavior of the semi-Dirac materials, photonic application concepts such as beam deflectors, beam splitters, and light focusing are proposed. Furthermore, to the best of our knowledge, semi-Dirac cone dispersion is also experimentally demonstrated for the first time by including negative, zero, and positive refraction states of the given material.

Fermion masses through four-fermion condensates

Energy Technology Data Exchange (ETDEWEB)

Ayyar, Venkitesh [Department of Physics, Duke University,Science Drive, Durham, NC 27708 (United States); Chandrasekharan, Shailesh [Department of Physics, Duke University,Science Drive, Durham, NC 27708 (United States); Center for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore, 560012 (India)

2016-10-12

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.

Unconventional superconductivity in a two-dimensional repulsive gas of fermions with spin-orbit coupling

Science.gov (United States)

Wang, Luyang; Vafek, Oskar

2014-02-01

We investigate the superconducting instability of a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling αR. Using renormalization group approach, we find the superconducting transition temperature as a function of the dimensionless ratio Θ=1}/{2}mαR2/EF where EF = 0 when the smaller Fermi surface shrinks to a (Dirac) point. The general trend is that superconductivity is enhanced as Θ increases, but in an intermediate regime Θ ∼ 0.1, a dome-like behavior appears. At a very small value of Θ, the angular momentum channel jz in which superconductivity occurs is quite high. With increasing Θ, jz decreases with a step of 2 down to jz = 6, after which we find the sequence jz = 6, 4, 6, 2, the last value of which continues to Θ → ∞. In an extended range of Θ, the superconducting gap predominantly resides on the large Fermi surface, while Josephson coupling induces a much smaller gap on the small Fermi surface. Below the superconducting transition temperature, we apply mean field theory to derive the self-consistent equations and find the condensation energies. The state with the lowest condensation energy is an unconventional superconducting state which breaks time-reversal symmetry, and in which singlet and triplet pairings are mixed. In general, these states are topologically nontrivial, and the Chern number of the state with total angular momentum jz is C = 2jz.

Electrical and thermoelectric transport properties of two-dimensional fermionic systems with k-cubic spin-orbit coupling.

Science.gov (United States)

Mawrie, Alestin; Verma, Sonu; Ghosh, Tarun Kanti

2017-09-01

We investigate effect of k-cubic spin-orbit interaction on electrical and thermoelectric transport properties of two-dimensional fermionic systems. We obtain exact analytical expressions of the inverse relaxation time (IRT) and the Drude conductivity for long-range Coulomb and short-range delta scattering potentials. The IRT reveals that the scattering is completely suppressed along the three directions θ = (2n+1)π/3 with n=1,2,3. We also obtain analytical results of the thermopower and thermal conductivity at low temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz law, even in the presence of k-cubic Rashba spin-orbit interaction (RSOI) at low temperature. In the presence of quantizing magnetic field, the signature of the RSOI is revealed through the appearance of the beating pattern in the Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in low magnetic field regime. The empirical formulae for the SdH oscillation frequencies accurately describe the locations of the beating nodes. The beating pattern in magnetothermoelectric measurement can be used to extract the spin-orbit coupling constant. © 2017 IOP Publishing Ltd.

Electrical and thermoelectric transport properties of two-dimensional fermionic systems with k-cubic spin-orbit coupling

Science.gov (United States)

Mawrie, Alestin; Verma, Sonu; Kanti Ghosh, Tarun

2017-11-01

We investigate the effect of k-cubic spin-orbit interaction on the electrical and thermoelectric transport properties of two-dimensional fermionic systems. We obtain exact analytical expressions of the inverse relaxation time (IRT) and the Drude conductivity for long-range Coulomb and short-range delta scattering potentials. The IRT reveals that the scattering is completely suppressed along the three directions θ^\\prime = (2n+1)π/3 with n=1, 2, 3 . We also obtain analytical results of the thermopower and thermal conductivity at low temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz law, even in the presence of k-cubic Rashba spin-orbit interaction (RSOI) at low temperature. In the presence of a quantizing magnetic field, the signature of the RSOI is revealed through the appearance of the beating pattern in the Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in the low magnetic field regime. The empirical formulae for the SdH oscillation frequencies accurately describe the locations of the beating nodes. The beating pattern in magnetothermoelectric measurement can be used to extract the spin-orbit coupling constant.

Dirac charge dynamics in graphene by infrared spectroscopy

International Nuclear Information System (INIS)

Martin, Michael C; Li, Z.Q.; Henriksen, E.A.; Jiang, Z.; Hao, Z.; Martin, Michael C; Kim, P.; Stormer, H.L.; Basov, Dimitri N.

2008-01-01

A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schroedinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations. Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, free-standing graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene

Eguchi-Kawai reduction with one flavor of adjoint Moebius fermion

OpenAIRE

Cunningham, William; Giedt, Joel

2013-01-01

We study the single site lattice gauge theory of SU(N) coupled to one Dirac flavor of fermion in the adjoint representation. We utilize M\\"obius fermions for this study, and accelerate the calculation with graphics processing units (GPUs). Our Monte Carlo simulations indicate that for sufficiently large inverse 't Hooft coupling b = 1/g^2 N, and for N \\leq 10 the distribution of traced Polyakov loops has "fingers" that extend from the origin. However, in the massless case the distribution of ...

Pressure induced superconductivity in the antiferromagnetic Dirac material BaMnBi2

OpenAIRE

Huimin Chen; Lin Li; Qinqing Zhu; Jinhu Yang; Bin Chen; Qianhui Mao; Jianhua Du; Hangdong Wang; Minghu Fang

2017-01-01

The so-called Dirac materials such as graphene and topological insulators are a new class of matter different from conventional metals and (doped) semiconductors. Superconductivity induced by doing or applying pressure in these systems may be unconventional, or host mysterious Majorana fermions. Here, we report a successfully observation of pressure-induced superconductivity in an antiferromagnetic Dirac material BaMnBi2 with T c of ~4?K at 2.6?GPa. Both the higher upper critical field, ? 0 H...

Arbitrary spin fermions on the lattice

International Nuclear Information System (INIS)

Bullinaria, J.A.

1985-01-01

Lattice actions are constructed for free Dirac and Majorana fermions of arbitrary (half-integer) spin various extensions of the spin 1/2 Kogut-Susskind, Kaehler and Wilson formalisms. In each case, the spectrum degeneracy and preservation of gauge invariance is analysed, and the equivalence or non-equivalence to previously constructed actions is determined. The Kogut-Susskind and lattice Kaehler actions are then written explicitly in terms of spinors to demonstrate how the degenerate fermions couple on the lattice and how the original spinorial actions are recovered (or to recovered) in the continuum limit. Both degenerate and non-degenerate mass terms are dealt with and the various U(1) invariances of the lattice actions are pointed out

The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

International Nuclear Information System (INIS)

Mourad, J.; Sazdjian, H.

1994-01-01

The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

Fermion families from two layer warped extra dimensions

International Nuclear Information System (INIS)

Guo Zhiqiang; Ma BoQiang

2008-01-01

In extra dimensions, the quark and lepton mass hierarchy can be reproduced from the same order bulk mass parameters, and standard model fermion families can be generated from one generation in the high dimensional space. We try to explain the origin of the same order bulk mass parameters and address the family replication puzzle simultaneously. We show that they correlate with each other. We construct models that families are generated from extra dimensional space, and in the meantime the bulk mass parameters of same order emerge naturally. The interesting point is that the bulk mass parameters, which are in same order, correspond to the eigenvalues of a Schroedinger-like equation. We also discuss the problem existing in this approach.

Anomalous diffusion of fermions in superlattices

International Nuclear Information System (INIS)

Drozdz, S.; Okolowicz, J.; Srokowski, T.; Ploszajczak, M.

1996-03-01

Diffusion of fermions in the periodic two-dimensional lattice of fermions is studied. It is shown that effects connected with antisymmetrization of the wave function increase chaoticness of motion. Various types of anomalous diffusion, characterized by a power spectral analysis are found. The nonlocality of the Pauli potential destroys cantori in the phase space. Consequently, the diffusion process is dominated by long free paths and the power spectrum is logarithmic at small frequency limit. (author)

Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS.

Science.gov (United States)

Singha, Ratnadwip; Pariari, Arnab Kumar; Satpati, Biswarup; Mandal, Prabhat

2017-03-07

Whereas the discovery of Dirac- and Weyl-type excitations in electronic systems is a major breakthrough in recent condensed matter physics, finding appropriate materials for fundamental physics and technological applications is an experimental challenge. In all of the reported materials, linear dispersion survives only up to a few hundred millielectronvolts from the Dirac or Weyl nodes. On the other hand, real materials are subject to uncontrolled doping during preparation and thermal effect near room temperature can hinder the rich physics. In ZrSiS, angle-resolved photoemission spectroscopy measurements have shown an unusually robust linear dispersion (up to [Formula: see text]2 eV) with multiple nondegenerate Dirac nodes. In this context, we present the magnetotransport study on ZrSiS crystal, which represents a large family of materials ( WHM with W = Zr, Hf; H = Si, Ge, Sn; M = O, S, Se, Te) with identical band topology. Along with extremely large and nonsaturating magnetoresistance (MR), [Formula: see text]1.4 [Formula: see text] 10 5 % at 2 K and 9 T, it shows strong anisotropy, depending on the direction of the magnetic field. Quantum oscillation and Hall effect measurements have revealed large hole and small electron Fermi pockets. A nontrivial [Formula: see text] Berry phase confirms the Dirac fermionic nature for both types of charge carriers. The long-sought relativistic phenomenon of massless Dirac fermions, known as the Adler-Bell-Jackiw chiral anomaly, has also been observed.

Two-loop fermionic corrections to massive Bhabha scattering

Energy Technology Data Exchange (ETDEWEB)

Actis, S.; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Czakon, M. [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Institute of Nuclear Physics, NSCR DEMOKRITOS, Athens (Greece); Gluza, J. [Silesia Univ., Katowice (Poland). Inst. of Physics

2007-05-15

We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses m{sub e}, m{sub f} and the Mandelstam invariants s, t, u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales m{sup 2}{sub e}<fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions. (orig.)

Zero sound in a two-dimensional dipolar Fermi gas

NARCIS (Netherlands)

Lu, Z.K.; Matveenko, S.I.; Shlyapnikov, G.V.

2013-01-01

We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both

Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

Directory of Open Access Journals (Sweden)

Alex Thomson

2018-01-01

Full Text Available Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP^{1} theory of bosonic spinons coupled to a U(1 gauge field, and with a global SU(2 spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z_{2} topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette. Fluctuations about this π-flux state are described by (2+1-dimensional quantum chromodynamics (QCD_{3} with a SU(2 gauge group and N_{f}=2 flavors of massless Dirac fermions. It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017.PRXHAE2160-330810.1103/PhysRevX.7.031051] that this QCD_{3} theory describes the Néel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD_{3} and obtain fermionic dual descriptions of the phases with Z_{2} topological order obtained earlier using the bosonic CP^{1} theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1 gauge theory of the VBS state. The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

Transport properties of chiral fermions

Energy Technology Data Exchange (ETDEWEB)

Puhr, Matthias

2017-04-26

Anomalous transport phenomena have their origin in the chiral anomaly, the anomalous non-conservation of the axial charge, and can arise in systems with chiral fermions. The anomalous transport properties of free fermions are well understood, but little is known about possible corrections to the anomalous transport coefficients that can occur if the fermions are strongly interacting. The main goal of this thesis is to study anomalous transport effects in media with strongly interacting fermions. In particular, we investigate the Chiral Magnetic Effect (CME) in a Weyl Semimetal (WSM) and the Chiral Separation Effect (CSE) in finite-density Quantum Chromodynamics (QCD). The recently discovered WSMs are solid state crystals with low-energy excitations that behave like Weyl fermions. The inter-electron interaction in WSMs is typically very strong and non-perturbative calculations are needed to connect theory and experiment. To realistically model an interacting, parity-breaking WSM we use a tight-binding lattice Hamiltonian with Wilson-Dirac fermions. This model features a non-trivial phase diagram and has a phase (Aoki phase/axionic insulator phase) with spontaneously broken CP symmetry, corresponding to the phase with spontaneously broken chiral symmetry for interacting continuum Dirac fermions. We use a mean-field ansatz to study the CME in spatially modulated magnetic fields and find that it vanishes in the Aoki phase. Moreover, our calculations show that outside of the Aoki phase the electron interaction has only a minor influence on the CME. We observe no enhancement of the magnitude of the CME current. For our non-perturbative study of the CSE in QCD we use the framework of lattice QCD with overlap fermions. We work in the quenched approximation to avoid the sign problem that comes with introducing a finite chemical potential on the lattice. The overlap operator calls for the evaluation of the sign function of a matrix with a dimension proportional to the volume

Bragg diffraction of fermions at optical potentials; Braggbeugung von Fermionen an optischen Potentialen

Energy Technology Data Exchange (ETDEWEB)

Deh, Benjamin

2008-10-27

This thesis describes the Bragg diffraction of ultracold fermions at an optical potential. A moving optical lattice was created, by overlaying two slightly detuned lasers. Atoms can be diffracted at this lattice if the detuning fulfills the Bragg condition for resting atoms. This Bragg diffraction is analyzed systematically in this thesis. To this end Rabi oscillations between the diffraction states were driven, as well in the weakly interacting Bragg regime, as in the strongly interacting Kapitza-Dirac regime. Simulations, based on a driven two-, respectively multilevel-system describe the observed effects rather well. Furthermore, the temporal evolution of the diffracted states in the magnetic trapping potential was studied. The anharmonicity of the trap in use and the scattering cross section for p-wave collisions in a {sup 6}Li system was determined from the movement of these states. Moreover the momentum distribution of the fermions was measured with Bragg spectroscopy and first signs of Fermi degeneracy were found. Finally an interferometer with fermions was build, exhibiting a coherence time of more than 100 {mu}s. With this, the possibility for measurement and manipulation of ultracold fermions with Bragg diffraction could bee shown. (orig.)

Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.

Science.gov (United States)

Owerre, S A

2017-07-31

In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX 3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L  ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM  magnon edge modes.

Casimir energy of massless fermions in the Slab-bag

International Nuclear Information System (INIS)

Paola, R.D.M. de; Rodrigues, R.B.; Svaiter, N.F.

1999-04-01

The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space-time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta function regularization procedure is used and it is founded that the regularized zero-point energy density is finite for any number of space-time dimensions. We present a general expression for the Casimir energy for the fermionic field in such a situation. (author)

Renormalization group analysis of order parameter fluctuations in fermionic superfluids

International Nuclear Information System (INIS)

Obert, Benjamin

2014-01-01

In this work fluctuation effects in two interacting fermion systems exhibiting fermionic s-wave superfluidity are analyzed with a modern renormalization group method. A description in terms of a fermion-boson theory allows an investigation of order parameter fluctuations already on the one-loop level. In the first project a quantum phase transition between a semimetal and a s-wave superfluid in a Dirac cone model is studied. The interplay between fermions and quantum critical fluctuations close to and at the quantum critical point at zero and finite temperatures are studied within a coupled fermion-boson theory. At the quantum critical point non-Fermi liquid and non-Gaussian behaviour emerge. Close to criticality several quantities as the susceptibility show a power law behaviour with critical exponents. We find an infinite correlation length in the entire semimetallic ground state also away from the quantum critical point. In the second project, the ground state of an s-wave fermionic superfluid is investigated. Here, the mutual interplay between fermions and order parameter fluctuations is studied, especially the impact of massless Goldstone fluctuations, which occur due to spontaneous breaking of the continuous U(1)-symmetry. Fermionic gap and bosonic order parameter are distinguished. Furthermore, the bosonic order parameter is decomposed in transverse and longitudinal fluctuations. The mixing between transverse and longitudinal fluctuations is included in our description. Within a simple truncation of the fermion-boson RG flow, we describe the fermion-boson theory for the first time in a consistent manner. Several singularities appear due the Goldstone fluctuations, which partially cancel due to symmetry. Our RG flow captures the correct infrared asymptotics of the system, where the collective excitations act as an interacting Bose gas. Lowest order Ward identities and the massless Goldstone mode are fulfilled in our truncation.

Superconductivity induced by flexural modes in non-σh-symmetric Dirac-like two-dimensional materials: A theoretical study for silicene and germanene

Science.gov (United States)

Fischetti, Massimo V.; Polley, Arup

2018-04-01

In two-dimensional crystals that lack symmetry under reflections on the horizontal plane of the lattice (non-σh-symmetric), electrons can couple to flexural modes (ZA phonons) at first order. We show that in materials of this type that also exhibit a Dirac-like electron dispersion, the strong coupling can result in electron pairing mediated by these phonons, as long as the flexural modes are not damped or suppressed by additional interactions with a supporting substrate or gate insulator. We consider several models: The weak-coupling limit, which is applicable only in the case of gapped and parabolic materials, like stanene and HfSe2, thanks to the weak coupling; the full gap-equation, solved using the constant-gap approximation and considering statically screened interactions; its extensions to energy-dependent gap and to dynamic screening. We argue that in the case of silicene and germanene superconductivity mediated by this process can exhibit a critical temperature of a few degrees K, or even a few tens of degrees K when accounting for the effect of a high-dielectric-constant environment. We conclude that the electron/flexural-modes coupling should be included in studies of possible superconductivity in non-σh-symmetric two-dimensional crystals, even if alternative forms of coupling are considered.

Dirac Magnons in Honeycomb Ferromagnets

Directory of Open Access Journals (Sweden)

Sergey S. Pershoguba

2018-01-01

Full Text Available The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009RMPHAT0034-686110.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014ADPHAH0001-873210.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX_{3} (X=F, Cl, Br and I, that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956PHRVAO0031-899X10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956PHRVAO0031-899X10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr_{3} [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in

Dirac Magnons in Honeycomb Ferromagnets

Science.gov (United States)

Pershoguba, Sergey S.; Banerjee, Saikat; Lashley, J. C.; Park, Jihwey; Ågren, Hans; Aeppli, Gabriel; Balatsky, Alexander V.

2018-01-01

The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009), 10.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014), 10.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX3 (X =F , Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956), 10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956), 10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr3 [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in Ferromagnetic CrBr3 Studied by Inelastic Neutron Scattering: Spin-Wave Correlation

Fermion families and vacuum in the two measures theory

International Nuclear Information System (INIS)

Guendelman, E.; Kaganovich, A.

2005-01-01

We present an alternative gravity and matter fields theory where the consistency condition of equations of motion yields strong correlation between states of 'primordial' fermion fields and local value of the scalar fields (dilaton and Higgs) energy density. The same 'primordial' fermion field at different densities can be either in states of regular fermionic matter or in states presumably corresponding to the dark fermionic matter. In regime of the fermion densities typical for normal particle physics, each of the primordial fermions splits into three generations identified with regular fermions. When restricting ourselves to the first two fermion generations, the theory reproduces general relativity and regular particle theory. As fermion energy density is comparable with vacuum energy density, the theory allows new type of states. Such Cosmo-Low Energy Physics (CLEP) state is studied in the framework of the model where FRW universe filled with homogeneous scalar field and uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are drawn into cosmological expansion by means of dynamically changing their own parameters. Some of the features of the CLEP state in the late time universe: neutrino mass increases as α 3/2 (α = α(t) is the scale factor); its energy density scales as a sort of dark energy and approaches constant as α→∞; this cold dark matter possesses negative pressure and its equation of state approaches that of the cosmological constant as α→∞; the total energy density of such universe is less than it would be in the universe free of fermionic matter at all. The latter means that nonrelativistic neutrinos are able to produce expanding bubbles of the CLEP state playing the role of a true 'cosmological vacuum' surrounded by a 'regular' vacuum. (authors)

Fermionic Casimir effect with helix boundary condition

International Nuclear Information System (INIS)

Zhai, Xiang-hua; Li, Xin-zhou; Feng, Chao-Jun

2011-01-01

In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Feng and Li (Phys. Lett. B 691:167, 2010), Zhai et al. (Mod. Phys. Lett. A 26:669, 2011) is something like that between a Moebius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the (D+1)-dimensional space-time. For both massless and massive cases, there is a Z 2 symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that the Casimir force approaches the result of the force in the massless case when the mass tends to zero and vanishes when the mass tends to infinity. (orig.)

Hamiltonian formalism at light front for two-dimensional quantum electrodynamics equivalent to lorentz-covariant approach

CERN Document Server

Paston, S A; Prokhvatilov, E V

2002-01-01

The Hamiltonian, reproducing the results of the two-dimensional quantum electrodynamics in the Lorentz coordinates, is constructed on the light front. The procedure of bosonization and analysis of the boson perturbation theory in all the orders by the fermions mass are applied for this purpose. Besides the common terms, originating by the naive quantization on the light front, the obtained Hamiltonian contains an additional counterterm. It is proportional to the linear combination of the fermion zero modes (multiplied by a certain factor compensating the charge and fermion number). The coefficient before this counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the theta-vacuum and by the small fermion mass is linear by it

Born-Kothari Condensation for Fermions

Directory of Open Access Journals (Sweden)

Arnab Ghosh

2017-09-01

Full Text Available In the spirit of Bose–Einstein condensation, we present a detailed account of the statistical description of the condensation phenomena for a Fermi–Dirac gas following the works of Born and Kothari. For bosons, while the condensed phase below a certain critical temperature, permits macroscopic occupation at the lowest energy single particle state, for fermions, due to Pauli exclusion principle, the condensed phase occurs only in the form of a single occupancy dense modes at the highest energy state. In spite of these rudimentary differences, our recent findings [Ghosh and Ray, 2017] identify the foregoing phenomenon as condensation-like coherence among fermions in an analogous way to Bose–Einstein condensate which is collectively described by a coherent matter wave. To reach the above conclusion, we employ the close relationship between the statistical methods of bosonic and fermionic fields pioneered by Cahill and Glauber. In addition to our previous results, we described in this mini-review that the highest momentum (energy for individual fermions, prerequisite for the condensation process, can be specified in terms of the natural length and energy scales of the problem. The existence of such condensed phases, which are of obvious significance in the context of elementary particles, have also been scrutinized.

Photonic band structures in one-dimensional photonic crystals containing Dirac materials

International Nuclear Information System (INIS)

Wang, Lin; Wang, Li-Gang

2015-01-01

We have investigated the band structures of one-dimensional photonic crystals (1DPCs) composed of Dirac materials and ordinary dielectric media. It is found that there exist an omnidirectional passing band and a kind of special band, which result from the interaction of the evanescent and propagating waves. Due to the interface effect and strong dispersion, the electromagnetic fields inside the special bands are strongly enhanced. It is also shown that the properties of these bands are invariant upon the lattice constant but sensitive to the resonant conditions

Emergence of geometry: A two-dimensional toy model

International Nuclear Information System (INIS)

Alfaro, Jorge; Espriu, Domene; Puigdomenech, Daniel

2010-01-01

We review the similarities between the effective chiral Lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D)xGL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zweibein is generated from a topological theory without any preexisting metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several nonstandard features this simple toy model appears to be renormalizable and at long distances is described by an effective Lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared regulator. The low-energy expansion is valid for momenta k>M, i.e. for supra-horizon scales. We briefly discuss a possible implementation of a similar mechanism in four dimensions.

Two-dimensional Yang-Mills theory in the leading 1/N expansion

International Nuclear Information System (INIS)

Wu, T.T.

1977-01-01

Recent controversies about the gauge invariance of the two-dimensional SU(N) Yang-Mills theory in the 't Hooft limit of large N are resolved. The fermion (quark) propagator is found explicitly, and is qualitatively different from those in the previous literature. (Auth.)

Fermion-dyon dynamics in non-Abelian gauge theory

International Nuclear Information System (INIS)

Pant, P.C.; Pandey, V.P.; Rajput, B.S.

1999-01-01

The study of behaviour of a fermion in the field of non-Abelian dyon has been undertaken in Lagrangian and Hamiltonian formulation. Solving Dirac equation, expression for energy Eigen value has been obtained and the Hamiltonian of this system has been shown to involve spin as well as contribution of massive fields associated with these particles. By introducing suitable spinors, the Pauli equation for a dyon moving in the field of fermion has been solved in non-Abelian gauge gauge theory and it is shown that introduction of massive fields perceptibly modifies the energy Eigen value and Eigen function of bound states of the system. (author)

A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space

International Nuclear Information System (INIS)

Le, Van-Hoang; Nguyen, Thanh-Son

2011-01-01

We establish an explicit form of a non-Abelian SO(8) monopole in a 9-dimensional space and show that it is indeed a direct generalization of Dirac and Yang monopoles. Using the generalized Hurwitz transformation, we have found a connection between a 16-dimensional harmonic oscillator and a 9-dimensional hydrogenlike atom in the field of the SO(8) monopole (MICZ-Kepler problem). Using the built connection the group of dynamical symmetry of the 9-dimensional MICZ-Kepler problem is found as SO(10, 2).

A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

Energy Technology Data Exchange (ETDEWEB)

Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O. [UFMA, Sao Luis (Brazil); Passos, E. [UFCG, Campina Grande, PB (Brazil)

2013-07-01

Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10{sub 16}. (author)

A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

International Nuclear Information System (INIS)

Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O.; Passos, E.

2013-01-01

Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10 16 . (author)

Holographic Fermions in Anisotropic Einstein-Maxwell-Dilaton-Axion Theory

International Nuclear Information System (INIS)

Kuang, Xiao-Mei; Fang, Li-Qing

2015-01-01

We investigate the properties of the holographic Fermionic system dual to an anisotropic charged black brane bulk in Einstein-Maxwell-Dilaton-Axion gravity theory. We consider the minimal coupling between the Dirac field and the gauge field in the bulk gravity theory and mainly explore the dispersion relation exponents of the Green functions of the dual Fermionic operators in the dual field theory. We find that along both the anisotropic and the isotropic directions the Fermi momentum will be effected by the anisotropy of the bulk theory. However, the anisotropy has influence on the dispersion relation which is almost linear for massless Fermions with charge q=2. The universal properties that the mass and the charge of the Fermi possibly correspond to nonlinear dispersion relation are also investigated

Mass anomalous dimension in SU(2) with six fundamental fermions

DEFF Research Database (Denmark)

Bursa, Francis; Del Debbio, Luigi; Keegan, Liam

2010-01-01

We simulate SU(2) gauge theory with six massless fundamental Dirac fermions. We measure the running of the coupling and the mass in the Schroedinger Functional scheme. We observe very slow running of the coupling constant. We measure the mass anomalous dimension gamma, and find it is between 0.13...

Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

Science.gov (United States)

Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

2017-11-01

We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

Gapped fermionic spectrum from a domain wall in seven dimension

Science.gov (United States)

Mukhopadhyay, Subir; Rai, Nishal

2018-05-01

We obtain a domain wall solution in maximally gauged seven dimensional supergravity, which interpolates between two AdS spaces and spontaneously breaks a U (1) symmetry. We analyse frequency dependence of conductivity and find power law behaviour at low frequency. We consider certain fermions of supergravity in the background of this domain wall and compute holographic spectral function of the operators in the dual six dimensional theory. We find fermionic operators involving bosons with non-zero expectation value lead to gapped spectrum.

Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

International Nuclear Information System (INIS)

Krolikowski, W.

1983-01-01

A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

Stochastic methods for the fermion determinant in lattice quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Finkenrath, Jacob Friedrich

2015-02-17

In this thesis, algorithms in lattice quantum chromodynamics are presented by developing and using stochastic methods for fermion determinant ratios. For that an integral representation is proved which can be used also for non hermitian matrices. The stochastic estimation or the Monte Carlo integration of this integral representation introduces stochastic fluctuations which are controlled by using Domain Decomposition of the Dirac operator and introducing interpolation techniques. Determinant ratios of the lattice fermion operator, here the Wilson Dirac operator, are needed for corrections of the Boltzmann weight. These corrections have interesting applications e.g. in the mass by using mass reweighting. It will be shown that mass reweighting can be used e.g. to improve extrapolation in the light quark mass towards the chiral or physical point or to introduce an isospin breaking by splitting up the mass of the light quark. Furthermore the extraction of the light quark masses will be shown by using dynamical 2 flavor CLS ensembles. Stochastic estimation of determinant ratios can be used in Monte Carlo algorithms, e.g. in the Partial Stochastic Multi Step algorithm which can sample two mass-degenerate quarks. The idea is to propose a new configuration weighted by the pure gauge weight and including afterwards the fermion weight by using Metropolis accept-reject steps. It is shown by using an adequate interpolation with relative gauge fixing and a hierarchical filter structure that it is possible to simulate moderate lattices up to (2.1 fm){sup 4}. Furthermore the iteration of the pure gauge update can be increased which can decouple long autocorrelation times from the weighting with the fermions. Moreover a novel Hybrid Monte Carlo algorithm based on Domain Decomposition and combined with mass reweighting is presented. By using Domain Decomposition it is possible to split up the mass term in the Schur complement and the block operators. By introducing a higher mass

All-order renormalization of propagator matrix for Majorana fermions with inter-generation mixing

International Nuclear Information System (INIS)

Kniehl, Bernd A.

2014-04-01

We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.

An accelerated conjugate gradient algorithm to compute low-lying eigenvalues - a study for the Dirac operator in SU(2) lattice QCD

International Nuclear Information System (INIS)

Kalkreuter, T.; Simma, H.

1995-07-01

The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalizations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional SU(2) gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes 4 4 - 16 4 an acceleration of the pure CG method by a factor of 4 - 8 is found. (orig.)

Dirac neutrino masses from generalized supersymmetry breaking

International Nuclear Information System (INIS)

Demir, D.A.; Everett, L.L.; Langacker, P.

2007-12-01

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the Standard Model with a generalized supersymmetry breaking sector. If the usual superpotential Yukawa couplings are forbidden by the additional gauge symmetry (such as a U(1) ' ), effective Dirac mass terms involving the ''wrong Higgs'' field can arise either at tree level due to hard supersymmetry breaking fermion Yukawa couplings, or at one-loop due to nonanalytic or ''nonholomorphic'' soft supersymmetry breaking trilinear scalar couplings. As both of these operators are naturally suppressed in generic models of supersymmetry breaking, the resulting neutrino masses are naturally in the sub-eV range. The neutrino magnetic and electric dipole moments resulting from the radiative mechanism also vanish at one-loop order. (orig.)

Approaching the Dirac point in high-mobility multilayer epitaxial graphene

Czech Academy of Sciences Publication Activity Database

Orlita, Milan; Faugeras, C.; Plochocka, P.; Neugebauer, P.; Martinez, G.; Maude, D. K.; Barra, A. L.; Sprinkle, M.; Berger, C.; de Heer, W.A.; Potemski, M.

2008-01-01

Roč. 101, č. 26 (2008), 267601/1-267601/4 ISSN 0031-9007 R&D Projects: GA AV ČR KAN400100652 Grant - others:EU(XE) RITA -CT-2003-505474 Institutional research plan: CEZ:AV0Z10100521 Keywords : multilayer epitaxial graphene * Dirac fermions * magnetic field Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 7.180, year: 2008

Dirac spectral density and mass anomalous dimension in 2+1 flavor QCD

Directory of Open Access Journals (Sweden)

Nakayama Katsumasa

2018-01-01

Full Text Available We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings (a = 0:083; 0:055; 0:044 fm to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to O(α4s.

Lepton mixing and cancellation of the Dirac mass hierarchy in SO(10) GUTs with flavor symmetries T7 and Σ(81)

International Nuclear Information System (INIS)

Hagedorn, Claudia; Schmidt, Michael A.; Smirnov, Alexei Yu.

2009-01-01

In SO(10) grand unified theories the hierarchy which is present in the Dirac mass term of the neutrinos is generically as strong as the one in the up-type quark mass term. We propose a mechanism to partially or completely cancel this hierarchy in the light neutrino mass matrix in the seesaw context. The two main ingredients of the cancellation mechanism are the existence of three fermionic gauge singlets and of a discrete flavor symmetry G f which is broken at a higher scale than SO(10). Two realizations of the cancellation mechanism are presented. The realization based on the Frobenius group T 7 ≅Z 7 xZ 3 leads to a partial cancellation of the hierarchy and relates maximal 2-3 lepton mixing with the geometric hierarchy of the up-quark masses. In the realization with the group Σ(81) the cancellation is complete and tribimaximal lepton mixing is reproduced at the lowest order. In both cases, to fully accommodate the leptonic data we take into account additional effects such as effects of higher-dimensional operators involving more than one flavon. The heavy neutral fermion mass spectra are considered. For both realizations we analyze the flavon potential at the renormalizable level as well as ways to generate the Cabibbo angle.

The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry

Science.gov (United States)

He, Wen-Yu; Chan, C. T.

2015-01-01

We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states. PMID:25640993

Naturally light Dirac neutrino in Left-Right Symmetric Model

Energy Technology Data Exchange (ETDEWEB)

Borah, Debasish [Department of Physics, Indian Institute of Technology Guwahati, Assam-781039 (India); Dasgupta, Arnab, E-mail: dborah@iitg.ernet.in, E-mail: arnab.d@iopb.res.in [Institute of Physics, HBNI, Sachivalaya Marg, Bhubaneshwar-751005 (India)

2017-06-01

We study the possibility of generating tiny Dirac masses of neutrinos in Left-Right Symmetric Model (LRSM) without requiring the existence of any additional symmetries. The charged fermions acquire masses through a universal seesaw mechanism due to the presence of additional vector like fermions. The neutrinos acquire a one-loop Dirac mass from the same additional vector like charged leptons without requiring any additional discrete symmetries. The model can also be extended by an additional Z {sub 2} symmetry in order to have a scotogenic version of this scenario predicting a stable dark matter candidate. We show that the latest Planck upper bound on the effective number of relativistic degrees of freedom N {sub eff}=3.15 ± 0.23 tightly constrains the right sector gauge boson masses to be heavier than 3.548 TeV . This bound on gauge boson mass also affects the allowed values of right scalar doublet dark matter mass from the requirement of satisfying the Planck bound on dark matter relic abundance. We also discuss the possible implications of such a scenario in charged lepton flavour violation and generating observable electric dipole moment of leptons.

Photon-Assisted Spectroscopy of Dirac Electrons in Graphene

Directory of Open Access Journals (Sweden)

Abdelrazek A. S.

2012-01-01

Full Text Available The quantum Goos-Hanchen effect in graphene is investigated. The Goos-Hanchen phase shift is derived by solving the Dirac eigenvalue differential equation. This phase shift varies with the angle of incidence of the quasiparticle Dirac fermions on the bar- rier. Calculations show that the dependence of the phase shift on the angle of incidence is sensitive to the variation of the energy gap of graphene, the applied magnetic field and the frequency of the electromagnetic waves. The present results show that the con- ducting states in the sidebands is very effective in the phase shift for frequencies of the applied electromagnetic field. This investigation is very important for the application of graphene in nanoelectronics and nanophotonics.

A realistic pattern of fermion masses from a five-dimensional SO(10) model

International Nuclear Information System (INIS)

Feruglio, Ferruccio; Patel, Ketan M.; Vicino, Denise

2015-01-01

We provide a unified description of fermion masses and mixing angles in the framework of a supersymmetric grand unified SO(10) model with anarchic Yukawa couplings of order unity. The space-time is five dimensional and the extra flat spatial dimension is compactified on the orbifold S 1 /(Z 2 ×Z 2 ′ ), leading to Pati-Salam gauge symmetry on the boundary where Yukawa interactions are localised. The gauge symmetry breaking is completed by means of a rather economic scalar sector, avoiding the doublet-triplet splitting problem. The matter fields live in the bulk and their massless modes get exponential profiles, which naturally explain the mass hierarchy of the different fermion generations. Quarks and leptons properties are naturally reproduced by a mechanism, first proposed by Kitano and Li, that lifts the SO(10) degeneracy of bulk masses in terms of a single parameter. The model provides a realistic pattern of fermion masses and mixing angles for large values of tan β. It favours normally ordered neutrino mass spectrum with the lightest neutrino mass below 0.01 eV and no preference for leptonic CP violating phases. The right handed neutrino mass spectrum is very hierarchical and does not allow for thermal leptogenesis. We analyse several variants of the basic framework and find that the results concerning the fermion spectrum are remarkably stable.

Dirac mechanics and Landau two-fluid model in /sup 4/HeII

Energy Technology Data Exchange (ETDEWEB)

Rodriguez-Gomez, J [Instituto Universitario Pedagogico de Caracas (Venezuela). Dept. de Matematica y Fisica

1980-07-01

This paper is devoted to the development of the Dirac formalism for singular systems when applied to the Landau two-fluid model in superfluid helium. Notably, the Hamiltonian density is weakly zero (in the sense of Dirac). We obtain the physical and gauge variables and show that all the constraints are of first class and hence that the Dirac bracket coincides with the Poisson bracket. The quantization of this system is left for a future paper.

Strong correlations in few-fermion systems

Energy Technology Data Exchange (ETDEWEB)

Bergschneider, Andrea

2017-07-26

In this thesis, I report on the deterministic preparation and the observation of strongly correlated few-fermion systems in single and double-well potentials. In a first experiment, we studied a system of one impurity interacting with a number of majority atoms which we prepared in a single potential well in the one-dimensional limit. With increasing number of majority particles, we observed a decrease in the quasi-particle residue which is in agreement with expectations from the Anderson orthogonality catastrophe. In a second experiment, we prepared two fermions in a double-well potential which represents the fundamental building block of the Fermi-Hubbard model. By increasing the repulsion between the two fermions, we observed the crossover into the antiferromagnetic Mott-insulator regime. Furthermore, I describe a new imaging technique, which allows spin-resolved single-atom detection both in in-situ and in time-of-flight. We use this technique to investigate the emergence of momentum correlations of two repulsive fermions in the ground state of the double well. With the methods developed in this thesis, we have established a framework for quantum simulation of strongly correlated many-body systems in tunable potentials.

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

International Nuclear Information System (INIS)

Ourabah, Kamel; Tribeche, Mouloud

2014-01-01

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics. Starting from the q-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length. -- Highlights: •Thomas–Fermi approach for self-gravitating fermions. •A generalized Thomas–Fermi equation is derived. •Nonextensivity preserves a scaling property of this equation. •Nonextensive approach to Jeans’ instability of self-gravitating fermions. •It is found that nonextensivity makes the Fermionic system unstable at shorter scales

Two-body Dirac equations for nucleon-nucleon scattering

International Nuclear Information System (INIS)

Liu Bin; Crater, Horace

2003-01-01

We investigate the nucleon-nucleon interaction by using the meson exchange model and the two-body Dirac equations of constraint dynamics. This approach to the two-body problem has been successfully tested for QED and QCD relativistic bound states. An important question we wish to address is whether or not the two-body nucleon-nucleon scattering problem can be reasonably described in this approach as well. This test involves a number of related problems. First we must reduce our two-body Dirac equations exactly to a Schroedinger-like equation in such a way that allows us to use techniques to solve them already developed for Schroedinger-like systems in nonrelativistic quantum mechanics. Related to this, we present a new derivation of Calogero's variable phase shift differential equation for coupled Schroedinger-like equations. Then we determine if the use of nine meson exchanges in our equations gives a reasonable fit to the experimental scattering phase shifts for n-p scattering. The data involve seven angular momentum states including the singlet states 1 S 0 , 1 P 1 , 1 D 2 and the triplet states 3 P 0 , 3 P 1 , 3 S 1 , 3 D 1 . Two models that we have tested give us a fairly good fit. The parameters obtained by fitting the n-p experimental scattering phase shift give a fairly good prediction for most of the p-p experimental scattering phase shifts examined (for the singlet states 1 S 0 , 1 D 2 and triplet states 3 P 0 , 3 P 1 ). Thus the two-body Dirac equations of constraint dynamics present us with a fit that encourages the exploration of a more realistic model. We outline generalizations of the meson exchange model for invariant potentials that may possibly improve the fit

Dirac and non-Dirac conditions in the two-potential theory of magnetic charge

Science.gov (United States)

Scott, John; Evans, Timothy J.; Singleton, Douglas; Dzhunushaliev, Vladimir; Folomeev, Vladimir

2018-05-01

We investigate the Cabbibo-Ferrari, two-potential approach to magnetic charge coupled to two different complex scalar fields, Φ _1 and Φ _2, each having different electric and magnetic charges. The scalar field, Φ _1, is assumed to have a spontaneous symmetry breaking self-interaction potential which gives a mass to the "magnetic" gauge potential and "magnetic" photon, while the other "electric" gauge potential and "electric" photon remain massless. The magnetic photon is hidden until one reaches energies of the order of the magnetic photon rest mass. The second scalar field, Φ _2, is required in order to make the theory non-trivial. With only one field one can always use a duality rotation to rotate away either the electric or magnetic charge, and thus decouple either the associated electric or magnetic photon. In analyzing this system of two scalar fields in the Cabbibo-Ferrari approach we perform several duality and gauge transformations, which require introducing non-Dirac conditions on the initial electric and magnetic charges. We also find that due to the symmetry breaking the usual Dirac condition is altered to include the mass of the magnetic photon. We discuss the implications of these various conditions on the charges.

Mott Transition of Fermionic Atoms in a Three-Dimensional Optical Trap

International Nuclear Information System (INIS)

Helmes, R. W.; Rosch, A.; Costi, T. A.

2008-01-01

We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean-field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments

New solitons connected to the Dirac equation

International Nuclear Information System (INIS)

Grosse, H.

1984-01-01

Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)

Massive boson-fermion degeneracy and the early structure of the universe

International Nuclear Information System (INIS)

Kounnas, C.

2008-01-01

The existence of a new kind of massive boson-fermion symmetry is shown explicitly in the framework of the heterotic, type II and type II orientifold superstring theories. The target space-time is two-dimensional. Higher dimensional models are defined via large marginal deformations of J anti J-type. The spectrum of the initial undeformed two dimensional vacuum consists of massless boson degrees of freedom, while all massive boson and fermion degrees of freedom exhibit a new Massive Spectrum Degeneracy Symmetry (MSDS). This precise property, distinguishes the MSDS theories from the well known supersymmetric SUSY-theories. Some proposals are stated in the framework of these theories concerning the structure of: (i) The Early Non-singular Phase of the Universe, (ii) The two dimensional boundary theory of AdS 3 Black-Holes, (iii) Plausible applications of the MSDS theories in particle physics, alternative to SUSY. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF2I3

Directory of Open Access Journals (Sweden)

Akito Kobayashi, Shinya Katayama and Yoshikazu Suzumura

2009-01-01

Full Text Available The quasi-two-dimensional molecular conductor α-(BEDT-TTF2I3 exhibits anomalous transport phenomena where the temperature dependence of resistivity is weak but the ratio of the Hall coefficient at 10 K to that at room temperature is of the order of 104. These puzzling phenomena were solved by predicting massless Dirac fermions, whose motions are described using the tilted Weyl equation with anisotropic velocity. α-(BEDT-TTF2I3 is a unique material among several materials with Dirac fermions, i.e. graphene, bismuth, and quantum wells such as HgTe, from the view-points of both the structure and electronic states described as follows. α-(BEDT-TTF2I3 has the layered structure with highly two-dimensional massless Dirac fermions. The anisotropic velocity and incommensurate momenta of the contact points, ±k0, originate from the inequivalency of the BEDT-TTF sites in the unit cell, where ±k0 moves in the first Brillouin zone with increasing pressure. The massless Dirac fermions exist in the presence of the charge disproportionation and are robust against the increase in pressure. The electron densities on those inequivalent BEDT-TTF sites exhibit anomalous momentum distributions, reflecting the angular dependences of the wave functions around the contact points. Those unique electronic properties affect the spatial oscillations of the electron densities in the vicinity of an impurity. A marked behavior of the Hall coefficient, where the sign of the Hall coefficient reverses sharply but continuously at low temperatures around 5 K, is investigated by treating the interband effects of the magnetic field exactly. It is shown that such behavior is possible by assuming the existence of the extremely small amount of electron doping. The enhancement of the orbital diamagnetism is also expected. The results of the present research shed light on a new aspect of Dirac fermion physics, i.e. the emergence of unique electronic properties owing to the structure

Signatures of Dirac Cones in a DMRG Study of the Kagome Heisenberg Model

Directory of Open Access Journals (Sweden)

Yin-Chen He

2017-07-01

Full Text Available The antiferromagnetic spin-1/2 Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large-scale density matrix renormalization group simulations (DMRG on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum-dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a π-flux free-fermion model [the parton mean-field ansatz of a U(1 Dirac spin liquid].

Ground-state and dynamical properties of two-dimensional dipolar Fermi liquids

International Nuclear Information System (INIS)

Abedinpour, Saeed H.; Asgari, Reza; Tanatar, B.; Polini, Marco

2014-01-01

We study the ground-state properties of a two-dimensional spin-polarized fluid of dipolar fermions within the Euler–Lagrange Fermi-hypernetted-chain approximation. Our method is based on the solution of a scattering Schrödinger equation for the “pair amplitude” √(g(r)), where g(r) is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow–Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree–Fock limit at weak coupling. Very good agreement with recent results based on quantum Monte Carlo simulations is achieved over a wide range of coupling constants up to the liquid-to-crystal quantum phase transition. Using the fluctuation–dissipation theorem and a static approximation for the effective inter-particle interactions, we calculate the dynamical density–density response function, and furthermore demonstrate that an undamped zero-sound mode exists for any value of the interaction strength, down to infinitesimally weak couplings. -- Highlights: •We have studied the ground state properties of a strongly correlated two-dimensional fluid of dipolar fermions. •We have calculated the effective inter-particle interaction and the dynamical density–density response function. •We have shown that an undamped zero sound mode exists at any value of the interaction strength

Fermions in curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Lippoldt, Stefan

2016-01-21

In this thesis we study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin base transformations. We emphasize the advantages of the spin base invariant formalism both from a conceptual as well as from a practical viewpoint. This suggests that local spin base invariance should be added to the list of (effective) properties of (quantum) gravity theories. We find support for this viewpoint by the explicit construction of a global realization of the Clifford algebra on a 2-sphere which is impossible in the spin-base non-invariant vielbein formalism. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vielbein field is not required. We disclose the hidden spin base invariance of the vielbein formalism. Explicit formulas for the spin connection as a function of the Dirac matrices are found. This connection consists of a canonical part that is completely fixed in terms of the Dirac matrices and a free part that can be interpreted as spin torsion. The common Lorentz symmetric gauge for the vielbein is constructed for the Dirac matrices, even for metrics which are not linearly connected. Under certain criteria, it constitutes the simplest possible gauge, demonstrating why this gauge is so useful. Using the spin base formulation for building a field theory of quantized gravity and matter fields, we show that it suffices to quantize the metric and the matter fields. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions. Hence, in the second part of this thesis we critically examine the gauge, and the field-parametrization dependence of renormalization group flows in the vicinity of non-Gaussian fixed points in quantum gravity. While physical

Dirac state in a centrosymmetric superconductor α -PdBi2

Science.gov (United States)

Dimitri, Klauss; Hosen, M. Mofazzel; Dhakal, Gyanendra; Choi, Hongchul; Kabir, Firoza; Sims, Christopher; Kaczorowski, Dariusz; Durakiewicz, Tomasz; Zhu, Jian-Xin; Neupane, Madhab

2018-04-01

Topological superconductor (TSC) hosting Majorana fermions has been established as a milestone that may shift our scientific trajectory from research to applications in topological quantum computing. Recently, superconducting Pd-Bi binaries have attracted great attention as a possible medium for the TSC phase as a result of their large spin-orbit coupling strength. Here, we report a systematic high-resolution angle-resolved photoemission spectroscopy (ARPES) study on the normal state electronic structure of superconducting α -PdBi2 (Tc=1.7 K). Our results show the presence of Dirac states at higher-binding energy with the location of the Dirac point at 1.26 eV below the chemical potential at the zone center. Furthermore, the ARPES data indicate multiple band crossings at the chemical potential, consistent with the metallic behavior of α -PdBi2 . Our detailed experimental studies are complemented by first-principles calculations, which reveal the presence of surface Rashba states residing in the vicinity of the chemical potential. The obtained results provide an opportunity to investigate the relationship between superconductivity, topology, and the Majorana fermion, as well as explore pathways to possible future platforms for topological quantum computing.

Fermi-Dirac statistics plus liquid description of quark partons

International Nuclear Information System (INIS)

Buccella, F.; Migliore, G.; Tibullo, V.

1995-01-01

A previous approach with Fermi-Dirac distributions for fermion partons is here improved to comply with the expected low x behaviour of structure functions. We are so able to get a fair description of the unpolarized and polarized structure functions of the nucleons as well as of neutrino data. We cannot reach definite conclusions, but confirm our suspicion of a relationship between the defects in Gottfried and spin sum rules. (orig.)

Chirally improving Wilson fermions I. O(a) improvement

International Nuclear Information System (INIS)

Frezzotti, R.; Rossi, G.C.

2004-01-01

We show that it is possible to improve the chiral behaviour and the approach to the continuum limit of correlation functions in lattice QCD with Wilson fermions by taking arithmetic averages of correlators computed in theories regularized with Wilson terms of opposite sign. Improved hadronic masses and matrix elements can be obtained by similarly averaging the corresponding physical quantities separately computed within the two regularizations. To deal with the problems related to the spectrum of the Wilson-Dirac operator, which are particularly worrisome when Wilson and mass terms are such as to give contributions of opposite sign to the real part of the eigenvalues, we propose to use twisted-mass lattice QCD for the actual computation of the quantities taking part to the averages. The choice ±π/2 for the twisting angle is particularly interesting, as O(a) improved estimates of physical quantities can be obtained even without averaging data from lattice formulations with opposite Wilson terms. In all cases little or no extra computing power is necessary, compared to simulations with standard Wilson fermions or twisted-mass lattice QCD. (author)

Constructing anisotropic single-Dirac-cones in Bi(1-x)Sb(x) thin films.

Science.gov (United States)

Tang, Shuang; Dresselhaus, Mildred S

2012-04-11

The electronic band structures of Bi(1-x)Sb(x) thin films can be varied as a function of temperature, pressure, stoichiometry, film thickness, and growth orientation. We here show how different anisotropic single-Dirac-cones can be constructed in a Bi(1-x)Sb(x) thin film for different applications or research purposes. For predicting anisotropic single-Dirac-cones, we have developed an iterative-two-dimensional-two-band model to get a consistent inverse-effective-mass-tensor and band gap, which can be used in a general two-dimensional system that has a nonparabolic dispersion relation as in the Bi(1-x)Sb(x) thin film system. © 2012 American Chemical Society

Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

International Nuclear Information System (INIS)

Zhang Fulin; Song Ci; Chen Jingling

2009-01-01

The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum L. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed

Two-dimensional N = 2 Super-Yang-Mills Theory

Science.gov (United States)

August, Daniel; Wellegehausen, Björn; Wipf, Andreas

2018-03-01

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.

Phase diagram of the Dirac spectrum at nonzero chemical potential

International Nuclear Information System (INIS)

Osborn, J. C.; Splittorff, K.; Verbaarschot, J. J. M.

2008-01-01

The Dirac spectrum of QCD with dynamical fermions at nonzero chemical potential is characterized by three regions: a region with a constant eigenvalue density, a region where the eigenvalue density shows oscillations that grow exponentially with the volume and the remainder of the complex plane where the eigenvalue density is zero. In this paper we derive the phase diagram of the Dirac spectrum from a chiral Lagrangian. We show that the constant eigenvalue density corresponds to a pion condensed phase while the strongly oscillating region is given by a kaon condensed phase. The normal phase with nonzero chiral condensate but vanishing Bose condensates coincides with the region of the complex plane where there are no eigenvalues.

Linearized fermion-gravitation system in a (2+1)-dimensional space-time with Chern-Simons data

International Nuclear Information System (INIS)

Mello, E.R.B. de.

1990-01-01

The fermion-graviton system at linearized level in a (2+1)-dimensional space-time with the gravitational Chern-Simons term is studied. In this approximation it is shown that this system presents anomalous rotational properties and spin, in analogy with the gauge field-matter system. (A.C.A.S.) [pt

Extended nonabelian symmetries for free fermionic model

International Nuclear Information System (INIS)

Zaikov, R.P.

1993-08-01

The higher spin symmetry for both Dirac and Majorana massless free fermionic field models are considered. An infinite Lie algebra which is a linear realization of the higher spin extension of the cross products of the Virasoro and affine Kac-Moody algebras is obtained. The corresponding current algebra is closed which is not the case of analogous current algebra in the WZNW model. The gauging procedure for the higher spin symmetry is also given. (author). 12 refs

Fermion localization in higher curvature and scalar-tensor theories of gravity

Energy Technology Data Exchange (ETDEWEB)

Mitra, Joydip [Scottish Church College, Department of Physics, Kolkata (India); Paul, Tanmoy; SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)

2017-12-15

It is well known that, in a braneworld model, the localization of fermions on a lower dimensional submanifold (say a TeV 3-brane) is governed by the gravity in the bulk, which also determines the corresponding phenomenology on the brane. Here we consider a five dimensional warped spacetime where the bulk geometry is governed by higher curvature like F(R) gravity. In such a scenario, we explore the role of higher curvature terms on the localization of bulk fermions which in turn determines the effective radion-fermion coupling on the brane. Our result reveals that, for appropriate choices of the higher curvature parameter, the profiles of the massless chiral modes of the fermions may get localized near the TeV brane, while those for massive Kaluza-Klein (KK) fermions localize towards the Planck brane. We also explore these features in the dual scalar-tensor model by appropriate transformations. The localization property turns out to be identical in the two models. This rules out the possibility of any signature of massive KK fermions in TeV scale collider experiments due to higher curvature gravity effects. (orig.)

Accidental degeneracy of double Dirac cones in a phononic crystal

KAUST Repository

Chen, Ze-Guo; Ni, Xu; Wu, Ying; He, Cheng; Sun, Xiao-Chen; Zheng, Li-Yang; Lu, Ming-Hui; Chen, Yan-Feng

2014-01-01

Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.

Accidental degeneracy of double Dirac cones in a phononic crystal

KAUST Repository

Chen, Ze-Guo

2014-04-09

Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.

Fermion number non-conservation and cold neutral fermionic matter in (V-A) gauge theories

International Nuclear Information System (INIS)

Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Tokarev, V.F.

1987-01-01

It is shown that in four-dimensional abelian (V-A) theories, the ground state of cold neutral fermionic matter is an anomalous state containing domains of abnormal phase surrounded by the normal vacuum. Inside these domains, there exists a gauge field condensate which makes real fermions disappear both inside and outside the domains. In non-abelian theories, the abnormal matter is unstable in its turn, and the system rolls back down into the normal state with a small number of fermions above the topologically non-trivial vacuum. Thus, in several non-abelian gauge theories, the fermion number density of cold neutral matter cannot exceed some critical value. (orig.)

Free massless fermionic fields of arbitrary spin in d-dimensional anti-de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A

1988-04-25

Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d-2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.

Quantum transport through 3D Dirac materials