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Author: Grafiati

Published: 25 May 2024

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1

Rycerz, Adam. "Wiedemann–Franz Law for Massless Dirac Fermions with Implications for Graphene." Materials 14, no. 11 (May 21, 2021): 2704. http://dx.doi.org/10.3390/ma14112704.

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In the 2016 experiment by Crossno et al. the electronic contribution to the thermal conductivity of graphene was found to violate the well-known Wiedemann–Franz (WF) law for metals. At liquid nitrogen temperatures, the thermal to electrical conductivity ratio of charge-neutral samples was more than 10 times higher than predicted by the WF law, which was attributed to interactions between particles leading to collective behavior described by hydrodynamics. Here, we show, by adapting the handbook derivation of the WF law to the case of massless Dirac fermions, that significantly enhanced thermal conductivity should appear also in few- or even sub-kelvin temperatures, where the role of interactions can be neglected. The comparison with numerical results obtained within the Landauer–Büttiker formalism for rectangular and disk-shaped (Corbino) devices in ballistic graphene is also provided.

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2

Naito, Toshio, and Ryusei Doi. "Band Structure and Physical Properties of α-STF2I3: Dirac Electrons in Disordered Conduction Sheets." Crystals 10, no. 4 (April 2, 2020): 270. http://dx.doi.org/10.3390/cryst10040270.

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The compound being investigated is an organic charge-transfer complex of the unsymmetrical donor STF with I3 [STF = bis(ethylenedithio)diselenadithiafulvalene], which is isostructural with α-ET2I3 and α-BETS2I3 [ET = bis(ethylenedithio)tetrathiafulvalene, BETS = bis(ethylenedithio)tetraselenafulvalene]. According to recent studies, the calculated band structure should represent a zero-gap semiconductor at 1 bar that is similar to α-ET2I3 under high pressure (>15 kbar). Such materials have attracted extensive interest because the electrons at the Fermi level can be massless Dirac fermions (MDFs), with relativistic behaviors like those seen in graphene. In fact, α-STF2I3 exhibited nearly temperature-independent resistivity, ρ, (~100–300 K), a phenomenon that is widely observed in zero-gap semiconductors. The non-Arrhenius-type increase in ρ (<~100 K) was consistent with the characteristics of interacting MDFs. The paramagnetic susceptibility, χ, (2–300 K)—as well as the reflectivity, R and optical conductivity, σ, (25–300 K; 400–25,000 cm−1)—were also almost temperature independent. Furthermore, σ was practically independent of wavenumber at ~6000–15,000 cm−1. There was no structural transition based on X-ray studies (90–300 K). Considering all the electrical, magnetic, optical and structural properties of α-STF2I3 at 1 bar, it was concluded that the salt possesses a band structure characterized with Dirac cones, which was consistent with the calculation.

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3

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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4

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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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

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

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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34

Hesselmann, S., T. C. Lang, M. Schuler, S. Wessel, and A. M. Läuchli. "Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”." Science 366, no. 6470 (December 5, 2019): eaav6869. http://dx.doi.org/10.1126/science.aav6869.

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Tang et al. (Research Articles, 10 August 2018, p. 570) report on the properties of Dirac fermions with both on-site and Coulomb interactions. The substantial decrease, up to ~40%, of the Fermi velocity of Dirac fermions with on-site interaction is inconsistent with the numerical data near the Gross-Neveu quantum critical point. This results from an inappropriate finite-size extrapolation.

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35

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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36

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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37

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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38

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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39

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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40

Mizushima, T., and K. Machida. "Multifaceted properties of Andreev bound states: interplay of symmetry and topology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2125 (June 20, 2018): 20150355. http://dx.doi.org/10.1098/rsta.2015.0355.

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Andreev bound states (ABSs) ubiquitously emerge as a consequence of non-trivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties such as Majorana fermions and odd-frequency pairing. A unified concept behind ABSs originates from a soliton state in the one-dimensional Dirac equation with mass domain wall and interplay of ABSs with symmetry and topology enrich their physical characteristics. We make an overview of ABSs with a special focus on superfluid 3 He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as the mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity and the anomalous magnetic response. The marriage of the superfluid 3 He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with ABSs. This article is part of the theme issue ‘Andreev bound states’.

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41

Vien, V. V., and N. V. Soi. "Fermion mass and mixing in an extension of the standard model with D5 symmetry." Modern Physics Letters A 35, no. 04 (October 11, 2019): 2050003. http://dx.doi.org/10.1142/s0217732320500030.

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We suggest a renormalizable standard model (SM) extension based on [Formula: see text] symmetry which accommodates leptonic mass and mixing parameters with nonzero [Formula: see text] and Dirac CP violating phase. Both normal and inverted neutrino mass ordering as well as the smallness of the active neutrino masses are generated at leading order through type-I seesaw mechanism in which the obtained physical parameters are well consistent with the global fit of neutrino oscillation data [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)], while the quark masses are in good agreement with the recent experimental data [Particle Data Group (M. Tanabashi et al.), Phys. Rev. D 98, 030001 (2018)]. The model also predicts an effective Majorana neutrino mass parameter of [Formula: see text] for normal hierarchy and [Formula: see text] for inverted hierarchy which are all well below the most current upper limit given [P. F. de Salas et al., Front. Astron. Space Sci. 5, 36 (2018); CUORE Collab. (C. Alduino et al.), Phys. Rev. Lett. 120, 132501 (2018)] and beyond the reach of the present [Formula: see text] decay experiments.

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42

Vien, V. V., and D. P. Khoi. "Fermion masses and mixings in a 3-3-1 model withQ4symmetry." Modern Physics Letters A 34, no. 25 (August 20, 2019): 1950198. http://dx.doi.org/10.1142/s0217732319501980.

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We construct a renormalizable [Formula: see text] model with [Formula: see text] symmetry accommodating the observed pattern of fermion masses and mixings with Dirac CP violation phase. The smallness of the active neutrino masses arises from a combination of type I and type II seesaw mechanisms. Both normal and inverted neutrino mass ordering are viable in our model in which the obtained physical observables of the lepton sector are well consistent with the global fit of neutrino oscillation data [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)] while the CKM matrix is unity at tree level and the quark masses are in good agreement with the experimental data [Particle Data Group (M. Tanabashi et al.), Phys. Rev. D 98, 030001 (2018)]. Furthermore, the model also predicts an effective Majorana neutrino mass parameter of [Formula: see text] eV for normal hierarchy and [Formula: see text] for inverted hierarchy which are consistent with the constraints given in [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)].

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Xin, Na, James Lourembam, Piranavan Kumaravadivel, A. E. Kazantsev, Zefei Wu, Ciaran Mullan, Julien Barrier, et al. "Giant magnetoresistance of Dirac plasma in high-mobility graphene." Nature 616, no. 7956 (April 12, 2023): 270–74. http://dx.doi.org/10.1038/s41586-023-05807-0.

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AbstractThe most recognizable feature of graphene’s electronic spectrum is its Dirac point, around which interesting phenomena tend to cluster. At low temperatures, the intrinsic behaviour in this regime is often obscured by charge inhomogeneity1,2 but thermal excitations can overcome the disorder at elevated temperatures and create an electron–hole plasma of Dirac fermions. The Dirac plasma has been found to exhibit unusual properties, including quantum-critical scattering3–5 and hydrodynamic flow6–8. However, little is known about the plasma’s behaviour in magnetic fields. Here we report magnetotransport in this quantum-critical regime. In low fields, the plasma exhibits giant parabolic magnetoresistivity reaching more than 100 per cent in a magnetic field of 0.1 tesla at room temperature. This is orders-of-magnitude higher than magnetoresistivity found in any other system at such temperatures. We show that this behaviour is unique to monolayer graphene, being underpinned by its massless spectrum and ultrahigh mobility, despite frequent (Planckian limit) scattering3–5,9–14. With the onset of Landau quantization in a magnetic field of a few tesla, where the electron–hole plasma resides entirely on the zeroth Landau level, giant linear magnetoresistivity emerges. It is nearly independent of temperature and can be suppressed by proximity screening15, indicating a many-body origin. Clear parallels with magnetotransport in strange metals12–14 and so-called quantum linear magnetoresistance predicted for Weyl metals16 offer an interesting opportunity to further explore relevant physics using this well defined quantum-critical two-dimensional system.

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Rom, Samir, Santu Baidya, Subhro Bhattacharjee, and Tanusri Saha-Dasgupta. "Magnetism and unconventional topology in LaCoO₃/SrIrO₃ heterostructure." Applied Physics Letters 122, no. 2 (January 9, 2023): 021602. http://dx.doi.org/10.1063/5.0113188.

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Employing first-principles calculations, we provide microscopic insights on the curious magnetic and topological properties of LaCoO3/SrIrO3 heterostructure, which has been recently synthesized [Kumar Jaiswal et al., Adv. Mater. 34, 2109163 (2022)]. Our computational study unravels transfer of polar charge from SrIrO3 to LaCoO3, thereby reducing the Co valence from 3+ toward 2+, supporting the experimental findings. Our study further reveals the stabilization of the intermediate spin state of Co and strong ferromagnetic Co–Co coupling in the LaCoO3 block of the heterostructure. This, in turn, is found to induce ferromagnetism in the pseudo-tetragonally structured SrIrO3 in the heterostructure geometry, providing an understanding of the origin of magnetism, which is counter-intuitive as both LaCoO3 and SrIrO3 are nonmagnetic in bulk form. Most interestingly, the band structure of ferromagnetic, tetragonal structured SrIrO3 is found to exhibit unconventional topology, manifested as C = 2 double Weyl points, which leads to the observed anomalous Hall effect. Our finding of C = 2 double Weyl points, belonging to the class of charge-2 Dirac points, opens up the possibility of material realization of unconventional topological properties beyond the conventional Dirac and C = 1 Weyl points, which calls for future experiments.

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45

Rost, A. W., J. Kim, S. Suetsugu, V. Abdolazimi, K. Hayama, J. A. N. Bruin, C. Mühle, et al. "Inverse-perovskites A3BO (A = Sr, Ca, Eu/B = Pb, Sn): A platform for control of Dirac and Weyl Fermions." APL Materials 7, no. 12 (December 1, 2019): 121114. http://dx.doi.org/10.1063/1.5129695.

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46

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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47

Terashima, Taichi, Shinya Uji, Teng Wang, and Gang Mu. "Topological frequency shift of quantum oscillation in CaFeAsF." npj Quantum Materials 7, no. 1 (March 4, 2022). http://dx.doi.org/10.1038/s41535-022-00431-z.

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AbstractGuo, Alexandradinata, et al. have recently proposed that quantum-oscillation frequencies from Dirac/Weyl fermions exhibit a negative shift proportional to T2 because of the energy dependence of the effective mass peculiar to a linear band-dispersion. We have measured Shubnikov–de Haas oscillation in CaFeAsF up to T = 9 K. The frequency of the α Dirac electron exhibits a negative shift with increasing T, while that of the β Schrödinger hole does not. For T ⩾ 5 K where β is negligible, the α-frequency shift is proportional to T2 and its rate agrees with the theoretical prediction within experimental accuracy. At lower temperatures, the shifts of α and β deviate from theoretical expectations, which we ascribe to the inaccuracy in the frequency determination due to unfavorable interference between frequencies. Our results confirm that the topological frequency shift can be utilized to identify Dirac/Weyl fermions when quantum-oscillation frequencies can be determined accurately.

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48

Bercioux, D., D. F. Urban, H. Grabert, and W. Häusler. "Massless Dirac-Weyl fermions in aT3optical lattice." Physical Review A 80, no. 6 (December 1, 2009). http://dx.doi.org/10.1103/physreva.80.063603.

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49

Gao, Heng, Youngkuk Kim, Jörn W. F. Venderbos, C. L. Kane, E. J. Mele, Andrew M. Rappe, and Wei Ren. "Dirac-Weyl Semimetal: Coexistence of Dirac and Weyl Fermions in Polar Hexagonal ABC Crystals." Physical Review Letters 121, no. 10 (September 5, 2018). http://dx.doi.org/10.1103/physrevlett.121.106404.

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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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