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Journal articles on the topic 'Dirac and Weyl fermions'

Author: Grafiati

Published: 25 May 2024

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1

Ma, Tian-Chi, Jing-Nan Hu, Yuan Chen, Lei Shao, Xian-Ru Hu, and Jian-Bo Deng. "Coexistence of type-II and type-IV Dirac fermions in SrAgBi." Modern Physics Letters B 35, no. 11 (February 9, 2021): 2150181. http://dx.doi.org/10.1142/s0217984921501815.

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Relativistic massless Weyl and Dirac fermions have isotropic and linear dispersion relations to maintain Poincaré symmetry, which is the most basic symmetry in high-energy physics. The situation in condensed matter physics is less constrained; only certain subgroups of Poincaré symmetry — the 230 space groups that exist in 3D lattices — need be respected. Then, the free fermionic excitations that have no high-energy analogues could exist in solid state systems. Here, We discovered a type of nonlinear Dirac fermion without high-energy analogue in SrAgBi and named it type-IV Dirac fermion. The type-IV Dirac fermion has a nonlinear dispersion relationship and is similar to the type-II Dirac fermion, which has electron pocket and hole pocket. The effective model for the type-IV Dirac fermion is also found. It is worth pointing out that there is a type-II Dirac fermion near this new Dirac fermion. So we used two models to describe the coexistence of these two Dirac fermions. Topological surface states of these two Dirac points are also calculated. We envision that our findings will stimulate researchers to study novel physics of type-IV Dirac fermions, as well as the interplay of type-II and type-IV Dirac fermions.

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2

Pal, Palash B. "Dirac, Majorana, and Weyl fermions." American Journal of Physics 79, no. 5 (May 2011): 485–98. http://dx.doi.org/10.1119/1.3549729.

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3

ALONSO, J. L., J. L. CORTÉS, and E. RIVAS. "WEYL FERMION FUNCTIONAL INTEGRAL AND TWO-DIMENSIONAL GAUGE THEORIES." International Journal of Modern Physics A 05, no. 14 (July 20, 1990): 2839–51. http://dx.doi.org/10.1142/s0217751x90001331.

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In the path integral approach we introduce a general regularization scheme for a Weyl fermionic measure. This allows us to study the functional integral formulation of a two-dimensional U(1) gauge theory with an arbitrary content of left-handed and right-handed fermions. A particular result is that, in contrast with a regularization of the fermionic measure based on a unique Dirac operator, by taking the Dirac fermionic measure as a product of two independent Weyl fermionic measures a consistent and unitary result can be obtained for the Chiral Schwinger Model (CSM) as a byproduct of the arbitrariness in the definition of the fermionic measure.

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4

Huang, Silu, Jisun Kim, W. A. Shelton, E. W. Plummer, and Rongying Jin. "Nontrivial Berry phase in magnetic BaMnSb2 semimetal." Proceedings of the National Academy of Sciences 114, no. 24 (May 24, 2017): 6256–61. http://dx.doi.org/10.1073/pnas.1706657114.

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The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either time-reversal or inversion symmetry breaking to lift degeneracy at Dirac points. Here we demonstrate experimentally that canted antiferromagnetic BaMnSb2 is a 3D Weyl semimetal with a 2D electronic structure. The Shubnikov–de Hass oscillations of the magnetoresistance give nearly zero effective mass with high mobility and the nontrivial Berry phase. The ordered magnetic arrangement (ferromagnetic ordering in the ab plane and antiferromagnetic ordering along the c axis below 286 K) breaks the time-reversal symmetry, thus offering us an ideal platform to study magnetic Weyl fermions in a centrosymmetric material.

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5

Bonora, Loriano, Roberto Soldati, and Stav Zalel. "Dirac, Majorana, Weyl in 4D." Universe 6, no. 8 (August 4, 2020): 111. http://dx.doi.org/10.3390/universe6080111.

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This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4D. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularisations. Among various well known results we stress in particular the regularisation independence in perturbative approaches, while not all the regularisations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.

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6

Pandey, Mahul, and Sachindeo Vaidya. "Yang–Mills matrix mechanics and quantum phases." International Journal of Geometric Methods in Modern Physics 14, no. 08 (May 11, 2017): 1740009. http://dx.doi.org/10.1142/s0219887817400096.

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The [Formula: see text] Yang–Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The [Formula: see text] Yang–Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

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7

Chen, Xiaomei, and Rui Zhu. "Quantum Pumping with Adiabatically Modulated Barriers in Three-Band Pseudospin-1 Dirac–Weyl Systems." Entropy 21, no. 2 (February 22, 2019): 209. http://dx.doi.org/10.3390/e21020209.

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In this work, pumped currents of the adiabatically-driven double-barrier structure based on the pseudospin-1 Dirac–Weyl fermions are studied. As a result of the three-band dispersion and hence the unique properties of pseudospin-1 Dirac–Weyl quasiparticles, sharp current-direction reversal is found at certain parameter settings especially at the Dirac point of the band structure, where apexes of the two cones touch at the flat band. Such a behavior can be interpreted consistently by the Berry phase of the scattering matrix and the classical turnstile mechanism.

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8

HARADA, KOJI. "EQUIVALENCE BETWEEN THE WESS-ZUMINO-WITTEN MODEL AND TWO CHIRAL BOSONS." International Journal of Modern Physics A 06, no. 19 (August 10, 1991): 3399–418. http://dx.doi.org/10.1142/s0217751x91001659.

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We establish the formal equivalence of a bosonized Dirac fermion (the Wess-Zumino-Witten model) to two bosonized Weyl fermions (Sonnenschein’s chiral bosons) in the path integral framework. These two systems can be regarded as gauge-fixed systems of the same gauge-invariant theory. Factorization of the fermion determinant of QCD2 is naturally realized in terms of chiral bosonization, up to a contact term which is necessary for maintaining gauge invariance. Canonical quantization of the gauge-invariantly extended system is performed.

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9

Reis, João Alfíeres Andrade de Simões dos, and Marco Schreck. "Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos." Symmetry 11, no. 10 (September 24, 2019): 1197. http://dx.doi.org/10.3390/sym11101197.

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The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of N neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic N, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos.

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10

Gao, Lan-Lan, and Xu-Guang Huang. "Chiral Anomaly in Non-Relativistic Systems: Berry Curvature and Chiral Kinetic Theory." Chinese Physics Letters 39, no. 2 (February 1, 2022): 021101. http://dx.doi.org/10.1088/0256-307x/39/2/021101.

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Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac and Weyl fermions. In most typical cases, the Lorentz covariance is assumed and thus the linear dispersion relations are maintained. However, in realistic materials, such as Dirac and Weyl semimetals, the nonlinear dispersion relations appear naturally. We develop a kinetic framework to study the chiral anomaly for Weyl fermions with nonlinear dispersions using the methods of Wigner function and semi-classical equations of motion. In this framework, the chiral anomaly is sourced by Berry monopoles in momentum space and could be enhanced or suppressed due to the windings around the Berry monopoles. Our results can help understand the chiral anomaly-induced transport phenomena in non-relativistic systems.

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11

Lin, Zeren, and Zhirong Liu. "Spin-1 Dirac-Weyl fermions protected by bipartite symmetry." Journal of Chemical Physics 143, no. 21 (December 7, 2015): 214109. http://dx.doi.org/10.1063/1.4936774.

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12

MARTELLINI, M., A. SEDRAKYAN, and M. SPREAFICO. "THE DYNAMICS OF DIRAC FERMIONS ON SINGULAR SURFACES." International Journal of Modern Physics B 10, no. 18n19 (August 30, 1996): 2423–29. http://dx.doi.org/10.1142/s0217979296001082.

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The determinant of induced Dirac action for fermions living on a two-dimensional surface immersed with Whitney singularities into 3D Euclidean space is calculated exactly in Weyl invariant regularization.

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13

Bradlyn, Barry, Jennifer Cano, Zhijun Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. Andrei Bernevig. "Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals." Science 353, no. 6299 (July 21, 2016): aaf5037. http://dx.doi.org/10.1126/science.aaf5037.

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14

Weber, Chris P., Leslie M. Schoop, Stuart S. P. Parkin, Robert C. Newby, Alex Nateprov, Bettina Lotsch, Bala Murali Krishna Mariserla, et al. "Directly photoexcited Dirac and Weyl fermions in ZrSiS and NbAs." Applied Physics Letters 113, no. 22 (November 26, 2018): 221906. http://dx.doi.org/10.1063/1.5055207.

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15

Sedrakyan, A. G., and R. Stora. "Dirac and Weyl fermions coupled to two-dimensional surfaces: Determinants." Physics Letters B 188, no. 4 (April 1987): 442–46. http://dx.doi.org/10.1016/0370-2693(87)91645-5.

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16

Singha, Ratnadwip, Arnab Kumar Pariari, Biswarup Satpati, and Prabhat Mandal. "Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS." Proceedings of the National Academy of Sciences 114, no. 10 (February 21, 2017): 2468–73. http://dx.doi.org/10.1073/pnas.1618004114.

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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∼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 (WHMwithW= Zr, Hf;H= Si, Ge, Sn;M= O, S, Se, Te) with identical band topology. Along with extremely large and nonsaturating magnetoresistance (MR),∼1.4×105% 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 nontrivialπBerry 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.

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17

Nilforoushan, Niloufar, Michele Casula, Adriano Amaricci, Marco Caputo, Jonathan Caillaux, Lama Khalil, Evangelos Papalazarou, et al. "Moving Dirac nodes by chemical substitution." Proceedings of the National Academy of Sciences 118, no. 33 (August 12, 2021): e2108617118. http://dx.doi.org/10.1073/pnas.2108617118.

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Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, BaNiS2, through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of BaCo1−xNixS2 across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the Γ−M symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making BaCo1−xNixS2 a model system to functionalize Dirac materials by varying the strength of electron correlations.

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18

Grushevskaya, H. V., and G. G. Krylov. "Low frequency conductivity in monolayer graphene model with partial unfolding of Dirac bands." International Journal of Modern Physics B 30, no. 13 (May 19, 2016): 1642009. http://dx.doi.org/10.1142/s0217979216420091.

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A secondary quantized field gauge theory with a number of flavors [Formula: see text] has been proposed to describe monolayer graphene. Charge carriers in this graphene model are Majorana pseudo-fermions. Partial unfolding of Dirac bands proceeds from coupling between anti-ordered pseudo-spins and valley currents. Splitting of Dirac cone replicas on Weyl-like node and anti-node leads to polarization effects analogous to graphene doping.

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19

Wang, Chengyi. "Majorana fermions and its application on topological quantum computer." Theoretical and Natural Science 30, no. 1 (January 15, 2024): 154–58. http://dx.doi.org/10.54254/2753-8818/30/20241092.

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The majorana fermion represents a kind of particle which is its own antiparticle. This paper aims to analyze the majorana fermions from theoretical aspect and application aspect, including the derivation of Dirac equation and the practicality of topological quantum computer. This paper explores the idea of Majorana fermions from Dirac equation and the anyons which is an important quasi-particle to build a topological quantum computer. After that, the potentials of quantum computer are emphasized as well. Several current major difficulties faced by building a quantum computer have also been discussed, including the decoherence of qubit and the errors during the operation of qubit. The advantages of topological computer are mentioned as well, especially the high resistance to local perturbation. The important property of two-dimensional non-abelian anyons has been discussed as well. Finally, the important relation of majorana fermions with anyons are introduced and the reason why majorana fermions is important has also been revealed.

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20

Cheskis, Dima. "Magneto-Optical Tools to Study Effects in Dirac and Weyl Semimetals." Symmetry 12, no. 9 (August 25, 2020): 1412. http://dx.doi.org/10.3390/sym12091412.

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Research regarding topological Dirac and Weyl semimetals contributes to our understanding not only of the field of solid-state physics, but also the field of high-energy physics as the physics of Dirac and Weyl semimetals resembles the physics of Dirac and Weyl massless fermions. In condensed matter physics, the Weyl nodes are detached in momentum space and may be realized as emergent quasiparticles with a distinct chirality, left-handed or right-handed. These states lead to phenomena like the chiral anomaly and the anomalous Hall effect (AHE). Furthermore, the combination of quantum effects and magnetic effects in magnetic Weyl semimetals is very intriguing. Magneto-optical tools, which are usually used to study magnetic phenomena, also contribute to magnetic Weyl semimetals. Moreover, with the magneto-optical technique, it is possible to follow the dynamics of the processes and to study the lifetime of the Weyl states. In this work, we review and discuss the effects of using magneto-optical tools for studying quantum effects like the chiral anomaly or magnetic effects in magnetic Weyl and Dirac systems using the magneto-optical Kerr effect (MOKE) or Faraday systems including a single detection and imaging. Examples of using magneto-optical systems in the research of ultrafast magnetic dynamics of thin polycrystalline nickel and permaloy are reviewed as are the magnetic spatial dynamics by employing magneto-optical Kerr or Faraday microscopy tools with ferromagnetic thin films. Interestingly, the excitation of a circularly polarized femtosecond laser pulse could lead to the breakage of time-reversal symmetry and to the transformation of the Dirac state to the Floquet–Weyl semimetal state. The development of a suitable ultrafast magneto-optical system for Weyl systems is discussed, and the practical difficulties for the realization of such a system are considered.

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21

Hasan, M. Zahid, Guoqing Chang, Ilya Belopolski, Guang Bian, Su-Yang Xu, and Jia-Xin Yin. "Weyl, Dirac and high-fold chiral fermions in topological quantum matter." Nature Reviews Materials 6, no. 9 (April 26, 2021): 784–803. http://dx.doi.org/10.1038/s41578-021-00301-3.

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22

Kavalov, A. R., I. K. Kostov, and A. G. Sedrakyan. "Dynamics of Dirac and Weyl fermions on a two-dimensional surface." Physics Letters B 175, no. 3 (August 1986): 331–34. http://dx.doi.org/10.1016/0370-2693(86)90865-8.

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23

Hu, Jin, Su-Yang Xu, Ni Ni, and Zhiqiang Mao. "Transport of Topological Semimetals." Annual Review of Materials Research 49, no. 1 (July 2019): 207–52. http://dx.doi.org/10.1146/annurev-matsci-070218-010023.

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Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated. The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermions. Experimental studies have shown that relativistic fermions can result in a rich variety of exotic transport properties, e.g., extremely large magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect. In this review, we first briefly introduce band structural characteristics of each topological semimetal phase, then review the current studies on quantum oscillations and exotic transport properties of various topological semimetals, and finally provide a perspective of this area.

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24

Huang, Zhe, Xianbiao Shi, Gaoning Zhang, Zhengtai Liu, Soohyun Cho, Zhicheng Jiang, Zhonghao Liu, et al. "Photoemission Spectroscopic Evidence of Multiple Dirac Cones in Superconducting BaSn₃." Chinese Physics Letters 38, no. 10 (November 1, 2021): 107403. http://dx.doi.org/10.1088/0256-307x/38/10/107403.

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Signatures of topological superconductivity (TSC) in superconducting materials with topological nontrivial states prompt intensive researches recently. Utilizing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations, we demonstrate multiple Dirac fermions and surface states in superconductor BaSn3 with a critical transition temperature of about 4.4 K. We predict and then unveil the existence of two pairs of type-I topological Dirac fermions residing on the rotational axis. Type-II Dirac fermions protected by screw axis are confirmed in the same compound. Further calculation for the spin helical texture of the observed surface states originating from the Dirac fermions gives an opportunity for realization of TSC in one single material. Hosting multiple Dirac fermions and topological surface states, the intrinsic superconductor BaSn3 is expected to be a new platform for further investigation of topological quantum materials as well as TSC.

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25

Keles, Ahmet, and Erhai Zhao. "Weyl nodes in periodic structures of superconductors and spin-active materials." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2125 (June 20, 2018): 20150151. http://dx.doi.org/10.1098/rsta.2015.0151.

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Motivated by recent progress in epitaxial growth of proximity structures of s -wave superconductors (S) and spin-active materials (M), in this paper we show that certain periodic structures of S and M can behave effectively as superconductors with pairs of point nodes, near which the low-energy excitations are Weyl fermions. A simple model, where M is described by a Kronig–Penney potential with both spin–orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero-energy surface states in the form of open Fermi lines (Fermi arcs). As a second example, a lattice model with alternating layers of S and magnetic Z 2 topological insulators is solved. The calculated spectrum confirms previous predictions of Weyl nodes based on the tunnelling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors. This article is part of the theme issue ‘Andreev bound states’.

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26

Elbistan, Mahmut. "Weyl semimetal and topological numbers." International Journal of Modern Physics B 31, no. 29 (November 7, 2017): 1750221. http://dx.doi.org/10.1142/s0217979217502216.

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Generalized Dirac monopoles in momentum space are constructed in even [Formula: see text] dimensions from the Weyl Hamiltonian in terms of Green’s functions. In [Formula: see text] dimensions, the (unit) charge of the monopole is equal to both the winding number and the Chern number, expressed as the integral of the Berry curvature. Based on the equivalence of the Chern and winding numbers, a chirally coupled and Lorentz invariant field theory action is studied for the Weyl semimetal phase. At the one loop order, the effective action yields both the chiral magnetic effect and the anomalous Hall effect. The Chern number appears as a coefficient in the conductivity, thus emphasizes the role of topology. The anomalous contribution of chiral fermions to transport phenomena is reflected as the gauge anomaly with the Pfaffian invariant [Formula: see text]. Relevance of monopoles and Chern numbers for the semiclassical chiral kinetic theory is also discussed.

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27

Xiong, Guang-Hua, Chao-Yun Long, and He Su. "Thermodynamic properties of massless Dirac–Weyl fermions under the generalized uncertainty principle*." Chinese Physics B 30, no. 7 (July 1, 2021): 070302. http://dx.doi.org/10.1088/1674-1056/abe1aa.

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28

Volovik, G. E. "Dirac and Weyl Fermions: from the Gor’kov equations to the standard model." JETP Letters 105, no. 4 (February 2017): 273–77. http://dx.doi.org/10.1134/s0021364017040063.

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29

Giordano, Matteo, and Tamás Kovács. "Localization of Dirac Fermions in Finite-Temperature Gauge Theory." Universe 7, no. 6 (June 8, 2021): 194. http://dx.doi.org/10.3390/universe7060194.

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It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

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30

Apalkov, Vadim, Xue-Feng Wang, and Tapash Chakraborty. "COLLECTIVE EXCITATIONS OF DIRAC ELECTRONS IN GRAPHENE." International Journal of Modern Physics B 21, no. 08n09 (April 10, 2007): 1165–79. http://dx.doi.org/10.1142/s0217979207042604.

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Two-dimensional electrons in graphene are known to behave as massless fermions with Dirac-Weyl type linear dispersion near the Dirac crossing points. We have investigated the collective excitations of this system in the presence or absence of an external magnetic field. Unlike in the conventional two-dimensional electron system, the [Formula: see text] fractional quantum Hall state in graphene was found to be most stable in the n = 1 Landau level. In the zero field case, but in the presence of the spin-orbit interaction, an undamped plasmon mode was found to exist in the gap of the single-particle continuum.

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31

Glozman, Leonid. "Chiralspin Symmetry and Its Implications for QCD." Universe 5, no. 1 (January 19, 2019): 38. http://dx.doi.org/10.3390/universe5010038.

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In a local gauge-invariant theory with massless Dirac fermions, a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the fermion charge operator is invariant under a larger symmetry group, S U ( 2 N F ) , that includes chiral transformations as well as S U ( 2 ) C S chiralspin transformations that mix the right- and left-handed components of fermions. Consequently, a symmetry of the electric interaction, which is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows separating in some situations electric and magnetic contributions. In particular, in QCD, the chromo-magnetic interaction contributes only to the near-zero modes of the Dirac operator, while confining chromo-electric interaction contributes to all modes. At high temperatures, above the chiral restoration crossover, QCD exhibits approximate S U ( 2 ) C S and S U ( 2 N F ) symmetries that are incompatible with free deconfined quarks. Consequently, elementary objects in QCD in this regime are quarks with a definite chirality bound by the chromo-electric field, without the chromo-magnetic effects. In this regime, QCD can be described as a stringy fluid.

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32

KERLER, WERNER. "CHIRAL FERMION OPERATORS ON THE LATTICE." International Journal of Modern Physics A 18, no. 15 (June 20, 2003): 2565–90. http://dx.doi.org/10.1142/s0217751x03013910.

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We only require generalized chiral symmetry and γ5-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field. Spectral representations turn out to be a powerful tool for obtaining detailed properties of the operators and a general construction of them. A basic unitary operator is seen to play a central rôle in this context. We discuss a number of special cases of the operators and elaborate on various aspects of index relations. We also show that our weaker conditions lead still properly to Weyl fermions and to chiral gauge theories.

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33

Khalilov, V. R. "Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field." Modern Physics Letters A 32, no. 38 (December 14, 2017): 1750200. http://dx.doi.org/10.1142/s0217732317502005.

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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 [Formula: see text] 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.

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34

Volovik, G. E., and K. Zhang. "Lifshitz Transitions, Type-II Dirac and Weyl Fermions, Event Horizon and All That." Journal of Low Temperature Physics 189, no. 5-6 (October 16, 2017): 276–99. http://dx.doi.org/10.1007/s10909-017-1817-8.

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Zheng, Ren-fei, Lu Zhou, and Weiping Zhang. "A beam splitter for Dirac–Weyl fermions through the Goos–Hänchen-like shift." Physics Letters A 381, no. 45 (December 2017): 3798–804. http://dx.doi.org/10.1016/j.physleta.2017.10.011.

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36

Soodchomshom, Bumned. "Tunneling Conductance in Strained Graphene-Based Superconductor: Effect of Asymmetric Weyl–Dirac Fermions." Journal of Superconductivity and Novel Magnetism 24, no. 5 (December 30, 2010): 1715–24. http://dx.doi.org/10.1007/s10948-010-1091-3.

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37

Giombi, Simone, Igor Klebanov, and Zhong Tan. "The ABC of Higher-Spin AdS/CFT." Universe 4, no. 1 (January 19, 2018): 18. http://dx.doi.org/10.3390/universe4010018.

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In recent literature, one-loop tests of the higher-spin AdS d + 1 /CFT d correspondences were carried out. Here, we extend these results to a more general set of theories in d > 2 . First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of N free fermion fields. In addition to the case of N Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic and Majorana–Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories, which we call Type AB. Their spectrum includes fields of every half-integer spin, and they are expected to be related to the U ( N ) / O ( N ) singlet sector of the CFT of N free complex/real scalar and fermionic fields. Finally, we explore the Type C theories, which have been conjectured to be dual to the CFTs of p-form gauge fields, where p = d 2 − 1 . In most cases, we find that the free energies at O ( N 0 ) either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant G N ∼ 1 / ( N − k ) , we find the values k = − 1 , − 1 / 2 , 0 , 1 / 2 , 1 , 2 . Exceptions to this rule are the Type B and AB theories in odd d; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant.

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38

KHALILOV, V. R. "SCATTERING OF A SPIN-POLARIZED NEUTRAL FERMION WITH THE ANOMALOUS MAGNETIC MOMENT IN AN AHARONOV–CASHER CONFIGURATION." Modern Physics Letters A 23, no. 15 (May 20, 2008): 1093–104. http://dx.doi.org/10.1142/s021773230802690x.

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The scattering of a nonrelativistic neutral massive fermion having the anomalous magnetic moment (AMM) in an electric field of a uniformly charged long conducting thread aligned perpendicularly to the fermion motion is considered to study the so-called Aharonov–Casher (AC) effect by taking into account the particle spin. For this solution, the nonrelativistic Dirac–Pauli equation for a neutral massive fermion with AMM in (3+1) dimensions is found, which takes into account explicitly the particle spin and interaction between AMM of moving fermion and the electric field. Expressions for the scattering amplitude and the cross-section are obtained for spin-polarized massive neutral fermion scattered off the above conducting thread. We conclude that the scattering amplitude and cross-section of spin-polarized massive neutral fermions are influenced by the interaction of AMM of moving neutral fermions with the electric field as well as by the polarization of fermion beam in the initial state.

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39

Rogerio, R. J. Bueno. "From dipole spinors to a new class of mass dimension one fermions." Modern Physics Letters A 35, no. 39 (October 30, 2020): 2050319. http://dx.doi.org/10.1142/s0217732320503198.

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In this paper, we investigate a quite recent new class of spin one-half fermions, namely Ahluwalia class-7 spinors, endowed with mass dimensionality 1 rather than 3/2, being candidates to describe dark matter. Such spinors, under the Dirac adjoint structure, belongs to the Lounesto’s class-6, namely, dipole spinors. Up to our knowledge, dipole spinor fields have Weyl spinor fields as their most known representative, nonetheless, here we explore the dark counterpart of the dipole spinors, which represents eigenspinors of the chirality operator.

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40

Bonora, Loriano. "Perturbative and Non-Pertrubative Trace Anomalies." Symmetry 13, no. 7 (July 18, 2021): 1292. http://dx.doi.org/10.3390/sym13071292.

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We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case, we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach.

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Figueiredo, José L., João P. S. Bizarro, and Hugo Terças. "Weyl–Wigner description of massless Dirac plasmas: ab initio quantum plasmonics for monolayer graphene." New Journal of Physics 24, no. 2 (February 1, 2022): 023026. http://dx.doi.org/10.1088/1367-2630/ac5132.

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Abstract We derive, from first principles and using the Weyl–Wigner formalism, a fully quantum kinetic model describing the dynamics in phase space of Dirac electrons in single-layer graphene. In the limit ℏ → 0, we recover the well-known semiclassical Boltzmann equation, widely used in graphene plasmonics. The polarizability function is calculated and, as a benchmark, we retrieve the result based on the random-phase approximation. By keeping all orders in ℏ, we use the newly derived kinetic equation to construct a fluid model for macroscopic variables written in the pseudospin space. As we show, the novel ℏ-dependent terms can be written as corrections to the average current and pressure tensor. Upon linearization of the fluid equations, we obtain a quantum correction to the plasmon dispersion relation, of order ℏ 2, akin to the Bohm term of quantum plasmas. In addition, the average variables provide a way to examine the value of the effective hydrodynamic mass of the carriers. For the latter, we find a relation in which Drude’s mass is multiplied by the square of a velocity-dependent, Lorentz-like factor, with the speed of light replaced by the Fermi velocity, a feature stemming from the quasi-relativistic nature of the Dirac fermions.

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42

Vafek, Oskar, and Ashvin Vishwanath. "Dirac Fermions in Solids: From High-TcCuprates and Graphene to Topological Insulators and Weyl Semimetals." Annual Review of Condensed Matter Physics 5, no. 1 (March 2014): 83–112. http://dx.doi.org/10.1146/annurev-conmatphys-031113-133841.

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43

Giordano, Matteo, Tamás G. Kovács, and Ferenc Pittler. "Anderson localization in QCD-like theories." International Journal of Modern Physics A 29, no. 25 (October 6, 2014): 1445005. http://dx.doi.org/10.1142/s0217751x14450055.

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We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low end of the spectrum have been found in SU(2) Yang–Mills theory with overlap and staggered valence fermions as well as in Nf = 2+1 QCD with staggered quarks. We draw an analogy between the transition from localized to delocalized modes in the Dirac spectrum and the Anderson transition in electronic systems. The QCD transition turns out to be in the same universality class as the transition in the corresponding Anderson model. We also speculate on the possible physical relevance of this transition to QCD at high temperature and the possible finite temperature phase transition in QCD-like models with different fermion contents.

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44

Dūdėnas, Vytautas, and Thomas Gajdosik. "Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms." Lithuanian Journal of Physics 56, no. 3 (October 17, 2016): 149–63. http://dx.doi.org/10.3952/physics.v56i3.3364.

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We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.

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45

Leaw, Jia Ning, Ho-Kin Tang, Maxim Trushin, Fakher F. Assaad, and Shaffique Adam. "Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions." Proceedings of the National Academy of Sciences 116, no. 52 (December 9, 2019): 26431–34. http://dx.doi.org/10.1073/pnas.1913096116.

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Recent experimental [I. Joet al.,Phys. Rev. Lett.119, 016402 (2017)] and numerical [M. Ippoliti, S. D. Geraedts, R. N. Bhatt,Phys. Rev. B95, 201104 (2017)] evidence suggests an intriguing universal relationship between the Fermi surface anisotropy of the noninteracting parent 2-dimensional (2D) electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filling. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed [H. -K. Tanget al.,Science361, 570 (2018)] nonperturbative and numerically exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For theν=1/2composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual Halperin–Lee–Read state. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators, organic conductors, and magic-angle twisted bilayer graphene.

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46

Kang, Joon Sang, Dung Vu, and Joseph P. Heremans. "Identifying the Dirac point composition in Bi_1−xSb_x alloys using the temperature dependence of quantum oscillations." Journal of Applied Physics 130, no. 22 (December 14, 2021): 225106. http://dx.doi.org/10.1063/5.0068312.

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The thermal chiral anomaly is a new mechanism for thermal transport that occurs in Weyl semimetals (WSMs). It is attributed to the generation and annihilation of energy at Weyl points of opposite chirality. The effect was observed in the Bi1− xSb x alloy system, at x = 11% and 15%, which are topological insulators at zero field and driven into an ideal WSM phase by an external field. Given that the experimental uncertainty on x is of the order of 1%, any systematic study of the effect over a wider range of x requires precise knowledge of the transition composition xc at which the electronic bands at the L-point in these alloys have Dirac-like dispersions. At x > xc, the L-point bands are inverted and become topologically non-trivial. In the presence of a magnetic field along the trigonal direction, these alloys become WSMs. This paper describes how the temperature dependence of the frequency of the Shubnikov–de Haas oscillations F( x,T) at temperatures of the order of the cyclotron energy can be used to find xc and characterize the topology of the electronic Fermi surface. Semimetallic Bi1−xSbx alloys with topologically trivial bands have dF( x,T) /dT ≥ 0; those with Dirac/Weyl fermions display dF( x,T) /dT < 0.

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47

Lu, Hai-Zhou, and Shun-Qing Shen. "Weak antilocalization and interaction-induced localization of Dirac and Weyl Fermions in topological insulators and semimetals." Chinese Physics B 25, no. 11 (November 2016): 117202. http://dx.doi.org/10.1088/1674-1056/25/11/117202.

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48

Mavromatos, Nick E. "Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation." Journal of Physics: Conference Series 2038, no. 1 (October 1, 2021): 012019. http://dx.doi.org/10.1088/1742-6596/2038/1/012019.

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Abstract In this mini review, we discuss some recent developments regarding properties of (quantum) field-theory models containing anti-Hermitian Yukawa interactions between pseudoscalar fields (axions) and Dirac (or Majorana) fermions. Specifically, we first motivate physically such interactions, in the context of string-inspired low-energy effective field theories, involving right-handed neutrinos and axion fields. Then we proceed to discuss their formal consistency within the so-called Parity-Time-reversal(PT)-symmetry framework. Subsequently, we review dynamical mass generation, induced by the Yukawa interactions, for both fermions and axions. The Yukawa couplings are assumed weak, given that they are conjectured to have been generated by non-perturbative effects in the underlying microscopic string theory. The models under discussion contain, in addition to the Yukawa terms, also anti-Hermitian anomalous derivative couplings of the pseudoscalar fields to axial fermion currents, as well as interactions of the fermions with non-Hermitian axial backgrounds. We discuss the role of such additional couplings on the Yukawa-induced dynamically-generated masses. For the case where the fermions are right-handed neutrinos, we compare such masses with the radiative ones induced by both, the anti-Hermitian anomalous terms and the anti-Hermitian Yukawa interactions in phenomenologically relevant models.

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Matos, Tonatiuh, Omar Gallegos, and Pierre-Henri Chavanis. "Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times." European Physical Journal C 82, no. 10 (October 11, 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10853-5.

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AbstractUsing a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein–Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.

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50

Hoffmann, Felix, Martin Siebert, Antonia Duft, and Vojislav Krstić. "Fingerprints of magnetoinduced charge density waves in monolayer graphene beyond half filling." Scientific Reports 12, no. 1 (December 15, 2022). http://dx.doi.org/10.1038/s41598-022-26122-0.

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AbstractA charge density wave is a condensate of fermions, whose charge density shows a long-range periodic modulation. Such charge density wave can be principally described as a macroscopic quantum state and is known to occur by various formation mechanisms. These are the lattice deforming Peierls transition, the directional, fermionic wave vector orientation prone Fermi surface nesting or the generic charge ordering, which in contrast is associated solely with the undirected effective Coulomb interaction between fermions. In two-dimensional Dirac/Weyl-like systems, the existence of charge density waves is only theoretically predicted within the ultralow energy regime at half filling. Taking graphene as host of two-dimensional fermions described by a Dirac/Weyl Hamiltonian, we tuned indirectly the effective mutual Coulomb interaction between fermions through adsorption of tetracyanoquinodimethane on top in the low coverage limit. We thereby achieved the development of a novel, low-dimensional dissipative charge density wave of Weyl-like fermions, even beyond half filling with additional magneto-induced localization and quantization. This charge density wave appears both, in the electron and the hole spectrum.

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