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Journal articles on the topic 'Weyl fermion'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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1

Xu, Su-Yang, Ilya Belopolski, Daniel S. Sanchez, Chenglong Zhang, Guoqing Chang, Cheng Guo, Guang Bian, et al. "Experimental discovery of a topological Weyl semimetal state in TaP." Science Advances 1, no. 10 (November 2015): e1501092. http://dx.doi.org/10.1126/sciadv.1501092.

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Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of tantalum arsenide, tantalum phosphide (TaP), niobium arsenide, and niobium phosphide, was predicted as a Weyl semimetal candidates. We experimentally realize a Weyl semimetal state in TaP. Using photoemission spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk, and the Fermi arcs on the surface. Moreover, we find that the surface states show an unexpectedly rich structure, including both topological Fermi arcs and several topologically trivial closed contours in the vicinity of the Weyl points, which provides a promising platform to study the interplay between topological and trivial surface states on a Weyl semimetal’s surface. We directly demonstrate the bulk-boundary correspondence and establish the topologically nontrivial nature of the Weyl semimetal state in TaP, by resolving the net number of chiral edge modes on a closed path that encloses the Weyl node. This also provides, for the first time, an experimentally practical approach to demonstrating a bulk Weyl fermion from a surface state dispersion measured in photoemission.

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2

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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3

Chang, Guoqing, Su-Yang Xu, Daniel S. Sanchez, Shin-Ming Huang, Chi-Cheng Lee, Tay-Rong Chang, Guang Bian, et al. "A strongly robust type II Weyl fermion semimetal state in Ta3S2." Science Advances 2, no. 6 (June 2016): e1600295. http://dx.doi.org/10.1126/sciadv.1600295.

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Weyl semimetals are of great interest because they provide the first realization of the Weyl fermion, exhibit exotic quantum anomalies, and host Fermi arc surface states. The separation between Weyl nodes of opposite chirality gives a measure of the robustness of the Weyl semimetal state. To exploit the novel phenomena that arise from Weyl fermions in applications, it is crucially important to find robust separated Weyl nodes. We propose a methodology to design robust Weyl semimetals with well-separated Weyl nodes. Using this methodology as a guideline, we search among the material parameter space and identify by far the most robust and ideal Weyl semimetal candidate in the single-crystalline compound tantalum sulfide (Ta3S2) with new and novel properties beyond TaAs. Crucially, our results show that Ta3S2has the largestk-space separation between Weyl nodes among known Weyl semimetal candidates, which is about twice larger than the measured value in TaAs and 20 times larger than the predicted value in WTe2. Moreover, all Weyl nodes in Ta3S2are of type II. Therefore, Ta3S2is a type II Weyl semimetal. Furthermore, we predict that increasing the lattice by <4% can annihilate all Weyl nodes, driving a novel topological metal-to-insulator transition from a Weyl semimetal state to a topological insulator state. The robust type II Weyl semimetal state and the topological metal-to-insulator transition in Ta3S2are potentially useful in device applications. Our methodology can be generally applied to search for new Weyl semimetals.

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4

Lai, Hsin-Hua, Sarah E. Grefe, Silke Paschen, and Qimiao Si. "Weyl–Kondo semimetal in heavy-fermion systems." Proceedings of the National Academy of Sciences 115, no. 1 (December 18, 2017): 93–97. http://dx.doi.org/10.1073/pnas.1715851115.

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Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy-fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here, we advance a Weyl–Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near the Weyl nodes develop out of the Kondo effect, as do the surface states that feature Fermi arcs. We determine the key signatures of this phase, which are realized in the heavy-fermion semimetal Ce3Bi4Pd3. Our findings provide the much-needed theoretical foundation for the experimental search of topological metals with strong correlations and open up an avenue for systematic studies of such quantum phases that naturally entangle multiple degrees of freedom.

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5

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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6

XU, YE-JUN, JUN SONG, HONG-CHUN YUAN, HONG-YI FAN, and QIU-YU LIU. "QUANTIZATION SCHEME FOR FERMIONIC SYSTEM AND s-ORDERED OPERATOR EXPANSION FORMULA OF FERMIONIC DENSITY OPERATORS." Modern Physics Letters A 26, no. 11 (April 10, 2011): 833–42. http://dx.doi.org/10.1142/s0217732311035213.

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We introduce the generalized fermionic Wigner operator with an s parameter. Based on its remarkable properties, we establish one-to-one mapping between fermion operators and their s-parametrized pseudo-classical correspondence, which may involve fermionic Weyl pseudo-classical correspondence, P-representation and Q-representation in a unified way. Furthermore, starting with the projector of the fermionic coherent state, we obtain the s-ordered operator expansion formula of fermionic density operators, which includes normally ordered, antinormally ordered and Weyl ordered product of operators for different values of s. Applications in calculating some Fermi operators' s-ordered expansions are presented.

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7

Xu, Bing, Zhenyao Fang, Miguel-Ángel Sánchez-Martínez, Jorn W. F. Venderbos, Zhuoliang Ni, Tian Qiu, Kaustuv Manna, et al. "Optical signatures of multifold fermions in the chiral topological semimetal CoSi." Proceedings of the National Academy of Sciences 117, no. 44 (October 19, 2020): 27104–10. http://dx.doi.org/10.1073/pnas.2010752117.

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We report the optical conductivity in high-quality crystals of the chiral topological semimetal CoSi, which hosts exotic quasiparticles known as multifold fermions. We find that the optical response is separated into several distinct regions as a function of frequency, each dominated by different types of quasiparticles. The low-frequency intraband response is captured by a narrow Drude peak from a high-mobility electron pocket of double Weyl quasiparticles, and the temperature dependence of the spectral weight is consistent with its Fermi velocity. By subtracting the low-frequency sharp Drude and phonon peaks at low temperatures, we reveal two intermediate quasilinear interband contributions separated by a kink at 0.2 eV. Using Wannier tight-binding models based on first-principle calculations, we link the optical conductivity above and below 0.2 eV to interband transitions near the double Weyl fermion and a threefold fermion, respectively. We analyze and determine the chemical potential relative to the energy of the threefold fermion, revealing the importance of transitions between a linearly dispersing band and a flat band. More strikingly, below 0.1 eV our data are best explained if spin-orbit coupling is included, suggesting that at these energies, the optical response is governed by transitions between a previously unobserved fourfold spin-3/2 node and a Weyl node. Our comprehensive combined experimental and theoretical study provides a way to resolve different types of multifold fermions in CoSi at different energy. More broadly, our results provide the necessary basis to interpret the burgeoning set of optical and transport experiments in chiral topological semimetals.

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8

Volovik, G. E., and M. A. Zubkov. "Emergent Weyl spinors in multi-fermion systems." Nuclear Physics B 881 (April 2014): 514–38. http://dx.doi.org/10.1016/j.nuclphysb.2014.02.018.

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9

Sukhachov, P. O. "Gap Generation in Weyl Semimetals in a Model with Local Four-Fermion Interaction." Ukrainian Journal of Physics 59, no. 7 (July 2014): 696–705. http://dx.doi.org/10.15407/ujpe59.07.0696.

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10

Huang, Shin-Ming, Su-Yang Xu, Ilya Belopolski, Chi-Cheng Lee, Guoqing Chang, Tay-Rong Chang, BaoKai Wang, et al. "New type of Weyl semimetal with quadratic double Weyl fermions." Proceedings of the National Academy of Sciences 113, no. 5 (January 19, 2016): 1180–85. http://dx.doi.org/10.1073/pnas.1514581113.

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Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs.

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11

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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12

Wu, Hongbo, Da-Shuai Ma, Botao Fu, Wei Guo, and Yugui Yao. "Weyl Nodal Point–Line Fermion in Ferromagnetic Eu5Bi3." Journal of Physical Chemistry Letters 10, no. 10 (April 29, 2019): 2508–14. http://dx.doi.org/10.1021/acs.jpclett.9b00752.

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13

Sarkar, Sujit. "Quantum simulation of Dirac fermion mode, Majorana fermion mode and Majorana-Weyl fermion mode in cavity QED lattice." EPL (Europhysics Letters) 110, no. 6 (June 1, 2015): 64003. http://dx.doi.org/10.1209/0295-5075/110/64003.

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14

Banerjee, H., G. Bhattacharya, and R. Banerjee. "Gauge theory ofSU(2) Weyl fermion: Is it consistent?" Zeitschrift für Physik C Particles and Fields 45, no. 2 (June 1989): 253–60. http://dx.doi.org/10.1007/bf01674454.

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15

ZUBKOV, M. A. "CLASSIﬁCATION OF EMERGENT WEYL SPINORS IN MULTI-FERMION SYSTEMS." ПИСЬМА В ЖУРНАЛ ЭКСПЕРИМЕНТАЛЬНОЙ И ТЕОРЕТИЧЕСКОЙ ФИЗИКИ 113, no. 7-8(4) (2021): 448–49. http://dx.doi.org/10.31857/s1234567821070041.

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16

Zubkov, M. A. "Classification of Emergent Weyl Spinors in Multi-Fermion Systems." JETP Letters 113, no. 7 (March 29, 2021): 445–53. http://dx.doi.org/10.1134/s0021364021070031.

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17

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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18

Stone, Michael. "Berry phase and anomalous velocity of Weyl fermions and Maxwell photons." International Journal of Modern Physics B 30, no. 02 (January 20, 2016): 1550249. http://dx.doi.org/10.1142/s0217979215502495.

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We consider two systems of wave equations whose wave packet solutions have trajectories that are altered by the “anomalous velocity” effect of a Berry curvature. The first is the matrix Weyl equation describing cyclotron motion of a charged massless fermion. The second is Maxwell equations for the whispering-gallery modes of light in a cylindrical waveguide. In the case of the massless fermion, the anomalous velocity is obscured by the contribution from the magnetic moment. In the whispering-gallery modes, the anomalous velocity causes the circumferential light ray to creep up the cylinder at the rate of one wavelength per orbit, and can be identified as a continuous version of the Imbert–Federov effect.

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19

Roy, Ashim, and Pratul Bandyopadhyay. "Topological aspects of SU(2) Weyl fermion and global anomaly." Journal of Mathematical Physics 35, no. 6 (June 1994): 2818–27. http://dx.doi.org/10.1063/1.530488.

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20

Xu, S. Y., I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, et al. "Discovery of a Weyl fermion semimetal and topological Fermi arcs." Science 349, no. 6248 (July 16, 2015): 613–17. http://dx.doi.org/10.1126/science.aaa9297.

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21

Hasan, M. Zahid, Su-Yang Xu, Ilya Belopolski, and Shin-Ming Huang. "Discovery of Weyl Fermion Semimetals and Topological Fermi Arc States." Annual Review of Condensed Matter Physics 8, no. 1 (March 31, 2017): 289–309. http://dx.doi.org/10.1146/annurev-conmatphys-031016-025225.

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22

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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23

Belopolski, Ilya, Kaustuv Manna, Daniel S. Sanchez, Guoqing Chang, Benedikt Ernst, Jiaxin Yin, Songtian S. Zhang, et al. "Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet." Science 365, no. 6459 (September 19, 2019): 1278–81. http://dx.doi.org/10.1126/science.aav2327.

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Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co2MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in this magnet. Our experimental results suggest a rich interplay of strongly interacting electrons and topology in quantum matter.

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24

Ma, Qiong, Su-Yang Xu, Ching-Kit Chan, Cheng-Long Zhang, Guoqing Chang, Yuxuan Lin, Weiwei Xie, et al. "Direct optical detection of Weyl fermion chirality in a topological semimetal." Nature Physics 13, no. 9 (May 29, 2017): 842–47. http://dx.doi.org/10.1038/nphys4146.

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25

LV, MIN, and SHOU-CHENG ZHANG. "DIELECTRIC FUNCTION, FRIEDEL OSCILLATION AND PLASMONS IN WEYL SEMIMETALS." International Journal of Modern Physics B 27, no. 25 (September 12, 2013): 1350177. http://dx.doi.org/10.1142/s0217979213501774.

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We calculate the dielectric function of a Weyl semimetal at arbitrary momentum q and frequency ω within the random-phase approximation. Taking the static limit, we calculated the Friedel oscillation and found that: (1) For a single Weyl point, the oscillation ~ sin (2kFr)/r4 falls off faster by an 1/r factor than the one in traditional 3D systems ~ cos (2kFr)/r3. This difference arises from the suppression of backward scattering in Weyl fermion systems; (2) For Weyl semimetal with two Weyl points, there are additional oscillations decaying as cos (Q ⋅ r)/r3 and cos (Q ± 2kF) ⋅ r/r3, where Q is the momentum difference between the two Weyl points. We also calculated the plasmon dispersion and found features distinct from those of conventional 3D metals.

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26

SOO, CHOPIN, and LAY NAM CHANG. "A WEYL DESCRIPTION OF GRAVITY INTERACTIONS." International Journal of Modern Physics A 24, no. 18n19 (July 30, 2009): 3372–81. http://dx.doi.org/10.1142/s0217751x09046977.

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We compare the conventional description of the interaction of matter with the four known forces in the standard model with an alternative Weyl description in which the chiral coupling is extended to include gravity. The two are indistinguishable at the low energy classical level of equations of motion, but there are subtle differences at the quantum level when nonvanishing torsion and the Adler-Bell-Jackiw anomaly are taken into account. The spin current and energy-momentum of the chiral theory then contain non-Hermitian terms which are not present in the conventional theory. In the chiral alternative, CPT invariance is not automatic because chirality supersedes Hermiticity but full Lorentz invariance holds. New fermion loop processes associated with the theory are discussed together with a perturbative regularization which explicitly maintains the chiral nature and local symmetries of the theory.

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27

Davidson, Aharon, and Tomer Ygael. "Ricci Linear Weyl/Maxwell Mutual Sourcing." Universe 6, no. 9 (September 14, 2020): 151. http://dx.doi.org/10.3390/universe6090151.

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We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian is dynamical scalar field free, hosts no fermion matter fields, and Holdom kinetic mixing is switched off. The mutual sourcing term is then necessarily spacetime curvature (not just metric) dependent, and inevitably Ricci linear, suggesting that a non-vanishing spacetime curvature can in principle induce an electromagnetic current. In its mature form, however, the Weyl/Maxwell mutual sourcing idea serendipitously constitutes a novel variant of the gravitational Weyl-Dirac (incorporating Brans-Dicke) theory. Counter intuitively, and again exclusively in four dimensions, the optional quartic scalar potential gets consistently replaced by a Higgs-like potential, such that the co-divergence of the Maxwell vector field resembles a conformal vacuum expectation value.

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28

DICK, RAINER. "HALF-DIFFERENTIALS AND FERMION PROPAGATORS." Reviews in Mathematical Physics 07, no. 05 (July 1995): 689–707. http://dx.doi.org/10.1142/s0129055x9500027x.

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From a geometric point of view, massless spinors in 3+1 dimensions are composed of primary fields of weights [Formula: see text] and [Formula: see text], where the weights are defined with respect to diffeomorphisms of a sphere in momentum space. The Weyl equation thus appears as a consequence of the transformation behavior of local sections of half-canonical bundles under a change of charts. As a consequence, it is possible to impose covariant constraints on spinors of negative (positive) helicity in terms of (anti-)holomorphy conditions. Furthermore, the identification with half-differentials is employed to determine possible extensions of fermion propagators compatible with Lorentz covariance.

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29

Dzsaber, Sami, Xinlin Yan, Mathieu Taupin, Gaku Eguchi, Andrey Prokofiev, Toni Shiroka, Peter Blaha, et al. "Giant spontaneous Hall effect in a nonmagnetic Weyl–Kondo semimetal." Proceedings of the National Academy of Sciences 118, no. 8 (February 19, 2021): e2013386118. http://dx.doi.org/10.1073/pnas.2013386118.

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Nontrivial topology in condensed-matter systems enriches quantum states of matter to go beyond either the classification into metals and insulators in terms of conventional band theory or that of symmetry-broken phases by Landau’s order parameter framework. So far, focus has been on weakly interacting systems, and little is known about the limit of strong electron correlations. Heavy fermion systems are a highly versatile platform to explore this regime. Here we report the discovery of a giant spontaneous Hall effect in the Kondo semimetal Ce3Bi4Pd3 that is noncentrosymmetric but preserves time-reversal symmetry. We attribute this finding to Weyl nodes—singularities of the Berry curvature—that emerge in the immediate vicinity of the Fermi level due to the Kondo interaction. We stress that this phenomenon is distinct from the previously detected anomalous Hall effect in materials with broken time-reversal symmetry; instead, it manifests an extreme topological response that requires a beyond-perturbation-theory description of the previously proposed nonlinear Hall effect. The large magnitude of the effect in even tiny electric and zero magnetic fields as well as its robust bulk nature may aid the exploitation in topological quantum devices.

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30

Xu, Su-Yang, Nasser Alidoust, Ilya Belopolski, Zhujun Yuan, Guang Bian, Tay-Rong Chang, Hao Zheng, et al. "Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide." Nature Physics 11, no. 9 (August 17, 2015): 748–54. http://dx.doi.org/10.1038/nphys3437.

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31

Hasan, M. Zahid, Su-Yang Xu, and Guang Bian. "Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks." Physica Scripta T164 (September 3, 2015): 014001. http://dx.doi.org/10.1088/0031-8949/2015/t164/014001.

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32

Bonora, L., M. Cvitan, P. Dominis Prester, A. D. Pereira, S. Giaccari, and T. štemberga. "Pontryagin trace anomaly." EPJ Web of Conferences 182 (2018): 02100. http://dx.doi.org/10.1051/epjconf/201818202100.

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33

ZENKIN, S. V. "GENERAL FORM OF THE LATTICE FERMION ACTION." Modern Physics Letters A 06, no. 02 (January 20, 1991): 151–55. http://dx.doi.org/10.1142/s0217732391000105.

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A set of lattice fermion actions is found which are consistent with canonical quantization of fermion systems. A new type of non-local chirally invariant action determined by the Weyl quantization is found to be inconsistent with gauge invariance. This completes the demonstration of the inconsistency of the non-local actions. The other actions are of the generalized Wilson form and may have the Kogut-Susskind-like symmetry which forbids mass terms.

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34

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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35

Lin, Zhi. "Progress Review on Topological Properties of Heusler Materials." E3S Web of Conferences 213 (2020): 02016. http://dx.doi.org/10.1051/e3sconf/202021302016.

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Starting from crystal, electronic and magnetic structures of Heusler compounds, this paper studies the new topological materials related to Heusler compounds and their topological properties, such as anomalous Hall effect, skyrmions, chiral anomaly, Dirac fermion, Weyl fermion, transverse Nernst thermoelectric effect, thermal spintronics and topological surface states. It can be discovered that the topological state of Heusler compound can be well protected due to its high symmetry, thus producing rich topological properties. Heusler materials belonged to Weyl semimetals usually have strong anomalous Hall effect, and the Heusler materials with doping or Anomalous Nernst Effect (ANE) usually have higher thermoelectric figure of merit. These anomalous effects are closely related to the strong spin–orbit interaction. In application, people can use the non-dissipative edge state of quantum anomalous Hall effect to develop a new generation of low-energy transistors and electronic devices. The conversion efficiency of thermoelectric materials can be improved by ANE, and topological superconductivity can be used to promote the progress of quantum computation.

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36

SHIMA, KAZUNARI, and MOTOMU TSUDA. "LINEARIZING N=1 NONLINEAR SUPERSYMMETRY WITH HIGHER DERIVATIVE TERMS OF A NAMBU–GOLDSTONE FERMION." Modern Physics Letters A 19, no. 18 (June 14, 2004): 1357–63. http://dx.doi.org/10.1142/s0217732304013994.

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We investigate for N=1 supersymmetry (SUSY) the relation between a scalar supermultiplet of linear SUSY and a nonlinear (NL) SUSY model including apparently pathological higher derivative terms of a Nambu–Goldstone (N-G) fermion besides the Volkov–Akulov (V-A) action. SUSY invariant relations with higher derivative terms of the N-G fermion, which connect the linear and NL–SUSY models, are constructed at leading orders by heuristic arguments. We discuss a higher derivative action of the N-G fermion in the NL–SUSY model, which apparently includes a (Weyl) ghost field. By using this relation, we also explicitly prove an equivalence between the standard NL–SUSY V-A model and our NL–SUSY model with the pathological higher derivatives as an example with respect to the universality of NL–SUSY actions with the N-G fermion.

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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

HSU, STEPHEN D. H. "GAUGINO DETERMINANT IN SUPERSYMMETRIC YANG–MILLS THEORY." Modern Physics Letters A 13, no. 09 (March 21, 1998): 673–76. http://dx.doi.org/10.1142/s0217732398000723.

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We resolve an ambiguity in the sign of the determinant of a single Weyl fermion, such as the gaugino in supersymmetric models. Positivity of this determinant is necessary for the application of QCD inequalities and lattice Monte–Carlo methods to supersymmetric Yang–Mills models.

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39

Hongo, Masaru, and Yoshimasa Hidaka. "Anomaly-Induced Transport Phenomena from Imaginary-Time Formalism." Particles 2, no. 2 (May 16, 2019): 261–80. http://dx.doi.org/10.3390/particles2020018.

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A derivation of anomaly-induced transport phenomena—the chiral magnetic/vortical effect—is revisited based on the imaginary-time formalism of quantum field theory. Considering the simplest anomalous system composed of a single Weyl fermion, we provide two derivations: perturbative (one-loop) evaluation of the anomalous transport coefficient, and the anomaly matching for the local thermodynamic functional.

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40

NAGAHAMA, Y., S. OJIMA, and K. SAKAI. "FOUR-DIMENSIONAL U(1) AND GAUGE ANOMALIES IN THE THEORY WITH MIXING INTERACTIONS." Modern Physics Letters A 03, no. 05 (April 1988): 481–87. http://dx.doi.org/10.1142/s0217732388000581.

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We study the four-dimensional U(1) and gauge anomalies by Fujikawa method in the presence of the interactions which mix the Rarita-Schwinger field with the Weyl fermion. We obtain a nonvanishing contribution from these interactions in the case of U(1) anomaly, while there arises no anomalous term in the case of the gauge anomaly.

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41

Magnifico, Giuseppe, Marcello Dalmonte, Paolo Facchi, Saverio Pascazio, Francesco V. Pepe, and Elisa Ercolessi. "Real Time Dynamics and Confinement in the Zn Schwinger-Weyl lattice model for 1+1 QED." Quantum 4 (June 15, 2020): 281. http://dx.doi.org/10.22331/q-2020-06-15-281.

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We study the out-of-equilibrium properties of 1+1 dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian Zn gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.

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42

SOW, C. L., and T. T. TRUONG. "QUANTUM GROUP APPROACH TO A SOLUBLE VERTEX MODEL WITH GENERALIZED ICE RULE." International Journal of Modern Physics A 11, no. 10 (April 20, 1996): 1747–61. http://dx.doi.org/10.1142/s0217751x96000936.

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Using the representation of the quantum group SL q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

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43

Lin, Weinan, Liang Liu, Qing Liu, Lei Li, Xinyu Shu, Changjian Li, Qidong Xie, et al. "Electric Field Control of the Magnetic Weyl Fermion in an Epitaxial SrRuO 3 (111) Thin Film." Advanced Materials 33, no. 36 (July 24, 2021): 2101316. http://dx.doi.org/10.1002/adma.202101316.

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44

DRECHSLER, WOLFGANG. "WEYL INVARIANT STANDARD MODEL AND ITS SYMMETRY BREAKING." International Journal of Geometric Methods in Modern Physics 10, no. 06 (April 30, 2013): 1350022. http://dx.doi.org/10.1142/s0219887813500229.

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A standard model is formulated in a Weyl space, W4, yielding a Weyl covariant dynamics of massless chiral Dirac fermion fields for leptons and quarks as well as the gauge fields involved for the groups D(1) (Weyl), U(1)Y × SU (2)W (electroweak), SU (3)c (color), SO(3, 1) (gravity) and SO(4, 1) (strong interaction, symmetry breaking). The dynamics is based on a gauge and Weyl invariant Lagrangian density [Formula: see text]. Gravitation is included from the beginning as the gauge aspect of the Lorentz group which is here extended in the hadronic sector of the model to the ten-parameter SO(4, 1) de Sitter group. A part of the dynamics is, as usual, a scalar isospinor field ϕ being a section on a bundle related to the electroweak gauge group and to symmetry breaking. In parallel to ϕ on the leptonic side a section [Formula: see text] on the hadronic side is considered as part of the dynamics, governing the symmetry breaking SO(4, 1) → SO(3, 1) and recovering gravitation in the symmetry breaking limit outside the regions in space–time where strong interactions persist. Besides spin, isospin and helicity the Weyl weights determine the form of the contributions of fields in [Formula: see text]. Of particular interest is the appearance of a current–current self-interaction of quark fields allowed by the Weyl weight changing the debate about quark masses. In a second step the D(1)-Weyl symmetry is explicitly broken and a universal mass scale is established through the mass of the ϕ-field appearing in the symmetry breaking Lagrangian [Formula: see text]. The Weyl symmetry breaking is governed by the relation DμΦ2 = 0, where Φ is the norm of ϕ. After D(1) symmetry breaking the masses of the weak bosons and of the electron appear on the scene through the energy–momentum tensor of the ϕ-field.

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45

ARAI, ASAO. "GENERALIZED WEAK WEYL RELATION AND DECAY OF QUANTUM DYNAMICS." Reviews in Mathematical Physics 17, no. 09 (October 2005): 1071–109. http://dx.doi.org/10.1142/s0129055x05002479.

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Let H be a self-adjoint operator on a Hilbert space [Formula: see text], T be a symmetric operator on [Formula: see text] and K(t)(t ∈ ℝ) be a bounded self-adjoint operator on [Formula: see text]. We say that (T, H, K) obeys the generalized weak Weyl relation (GWWR) if e-itHD(T) ⊂ D(T) for all t ∈ ℝ and Te-itHψ = e-itH(T+K(t))ψ, ∀ψ ∈ D(T) (D(T) denotes the domain of T). In the context of quantum mechanics where H is the Hamiltonian of a quantum system, we call T a generalized time operator of H. We first investigate, in an abstract framework, mathematical structures and properties of triples (T, H, K) obeying the GWWR. These include the absolute continuity of the spectrum of H restricted to a closed subspace of [Formula: see text], an uncertainty relation between H and T (a "time-energy uncertainty relation"), the decay property of transition probabilities |〈ψ,e-itHϕ〉|2 as |t| → ∞ for all vectors ψ and ϕ in a subspace of [Formula: see text], where 〈·,·〉 denotes the inner product of [Formula: see text]. We describe methods to construct various examples of triples (T, H, K) obeying the GWWR. In particular, we show that there exist generalized time operators of second quantization operators on Fock spaces (full Fock spaces, boson Fock spaces and fermion Fock spaces) which may have applications to quantum field models with interactions.

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46

Franco, Nicolas. "Physical models from noncommutative causality." EPJ Web of Conferences 182 (2018): 02043. http://dx.doi.org/10.1051/epjconf/201818202043.

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We introduced few years ago a new notion of causality for noncommutative spacetimes directly related to the Dirac operator and the concept of Lorentzian spectral triple. In this paper, we review in a non-technical way the noncommutative causal structure of many toy models as almost commutative spacetimes and the Moyal-Weyl spacetime. We show that those models present some unexpected physical interpretations as a geometrical explanation of the Zitterbewegung trembling motion of a fermion as well as some geometrical constraints on translations and energy jumps of wave packets on the Moyal spacetime.

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47

van Delft, Maarten R., Sergio Pezzini, Markus König, Paul Tinnemans, Nigel E. Hussey, and Steffen Wiedmann. "Two- and Three-Dimensional Superconducting Phases in the Weyl Semimetal TaP at Ambient Pressure." Crystals 10, no. 4 (April 10, 2020): 288. http://dx.doi.org/10.3390/cryst10040288.

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The motivation to search for signatures of superconductivity in Weyl semi-metals and other topological phases lies in their potential for hosting exotic phenomena such as nonzero-momentum pairing or the Majorana fermion, a viable candidate for the ultimate realization of a scalable quantum computer. Until now, however, all known reports of superconductivity in type-I Weyl semi-metals have arisen through surface contact with a sharp tip, focused ion-beam surface treatment or the application of high pressures. Here, we demonstrate the observation of superconductivity in single crystals, even an as-grown crystal, of the Weyl semi-metal tantalum phosphide (TaP), at ambient pressure. A superconducting transition temperature, T c , varying between 1.7 and 5.3 K, is observed in different samples, both as-grown and microscopic samples processed with focused ion beam (FIB) etching. Our data show that the superconductivity present in the as-grown crystal is inhomogeneous yet three-dimensional. For samples fabricated with FIB, we observe, in addition to the three-dimensional superconductivity, a second superconducting phase that resides on the sample surface. Through measurements of the characteristic fields as a function of temperature and angle, we are able to confirm the dimensionality of the two distinct superconducting phases.

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48

Bytsenko, A. A., M. Chaichian, and A. E. Gonçalves. "Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants." International Journal of Modern Physics A 34, no. 11 (April 20, 2019): 1930060. http://dx.doi.org/10.1142/s0217751x19300060.

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In this paper we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson–fermion correspondence, the analytic torsion, the Chern–Simons and [Formula: see text] invariants, as well as the generating function associated to dimensions of the Hochschild homology of the crossed product [Formula: see text] ([Formula: see text] is the [Formula: see text]-Weyl algebra). After analyzing the Chern–Simons and [Formula: see text] invariants of Dirac operators by using irreducible [Formula: see text]-flat connections on locally symmetric manifolds of nonpositive section curvature, we describe the exponential action for the Chern–Simons theory.

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49

Hasan, M. Z., S.-Y. Xu, and G. Bian. "Corrigendum: Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks (2015 Phys. Scr. 2015 014001)." Physica Scripta T168 (October 21, 2016): 019501. http://dx.doi.org/10.1088/0031-8949/t168/1/019501.

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50

FALCO, L. DE, R. MIGNANI, and R. SCIPIONI. "FOCK SPACE FOR GENERALIZED STATISTICS AND BOSON-FERMION SUPERSELECTION RULE." Modern Physics Letters B 10, no. 21 (September 10, 1996): 1035–41. http://dx.doi.org/10.1142/s0217984996001176.

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We introduce a generalized Fock space for a recently proposed operatorial deformation of the Heisenberg-Weyl (HW) algebra, aimed at describing statistics different from the Bose or Fermi ones. The new Fock space is obtained by the tensor product of the usual Fock space and the space spanned by the eigenstates of the deformation operator ĝ. We prove a “statistical Ehrenfest-like theorem”, stating that the expectation values of the ladder operators of the generalized HW algebra — taken in the ĝ-subspace — are creation and annihilation operators defined in the usual Fock space and obeying the ordinary statistics, according to the ĝ-eigenvalues. Moreover, such a “statistics” operator ĝ can be regarded as the generator of a boson-fermion superselection rule. As a consequence, the generalized Fock space decomposes into incoherent sectors, and therefore one gets a density matrix diagonal in the ĝ eigenstates. This leads, under suitable conditions, to the possibility of continuously interpolating between different statistics. In particular, it is necessary to assume a nonstandard Liouville-Von Neumann equation for the density matrix, of the type already considered e.g. in the framework of quantum gravity. It is also preliminarily shown that our formalism leads in a natural way — due to the very properties of the operator ĝ — to a grading of the HW algebra, and therefore to a supersymmetrical scheme.

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