The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal

Nielsen, Holger Bech; Ninomiya, M.

doi:10.1016/0370-2693(83)91529-0

Cited by 1,709 publications

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References 9 publications

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“…In fact, the original attempt to realize Weyl fermions in 3D lattice systems results in the famous fermiondoubling theorem, which dictates the total number of Weyl nodes must be even 11 . This is related to another famous phenomena, the Adler-Bell-Jackiw anomaly (or chiral anomaly) 8 . Weyl Fermions have its handiness or chirality.…”

Section: Introductionmentioning

confidence: 99%

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

2011

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There have been lots of interest in pyrochlore Iridates A2Ir2O7 where both strong spin-orbital coupling and strong correlation are present. A recent LDA calculation 1 suggests that the system is likely in a novel three dimensional topological semi-metallic phase: a Weyl semi-metal. Such a system has zero carrier density and arrives at the quantum limit even in a weak magnetic field. In this paper we discuss two novel quantum effects of this system in a magnetic field: a pressure-induced anomalous Hall effect and a magnetic field induced charge density wave at the pinned wavevector connecting Weyl nodes with opposite chiralities. A general formula of the anomalous hall coefficients in a Weyl semi-metal is also given. Both proposed effects can be probed by experiments in the near future, and can be used to detect the Weyl semi-metal phase.

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Section: Introductionmentioning

confidence: 99%

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

2011

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“…4 Weyl semimetal (WSM) has linear despersion around two-fold degenerate band-crossing points, [5][6][7][8][9][10][11][12][13][14] and the Weyl point possesses a definite chirality of ±1, around which the quasiparticle excitation is anolog of Weyl fermions. 4,15 Furthermore, it could be viewed as the monopole of Berry flux in momentum space, and the two Weyl points with opposite chiralities correspond to the source and drain respectively. 16 The surface states of a WSM are Fermi arcs, which are open segments of Fermi surface connecting the projections of Weyl points of opposite chiralities on the two-dimentional (2D) surfaces.…”

Section: Introductionmentioning

confidence: 99%

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

Chen

Zhang

et al. 2017

J. Phys. Chem. C

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Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossing points with linear dispersion, around which the quasiparticles resemble the relativistic Dirac Fermions. It can be described by a 4 × 4 massless Dirac Hamiltonian which can be decomposed into a pair of Weyl points or gaped into an insulator. Thus, crystal symmetry is critical to guarantee the stable existence. On the contrary, by breaking crystal symmetry, a DSM may transform into a Weyl semimetal (WSM) or a topological insulator (TI). Here, by taking hexagonal LiAuSe as an example, we find that it is a starfruit shaped multiple nodal chain semimetal in the absence of spin-orbit coupling 1 arXiv:1712.01475v1 [cond-mat.mtrl-sci] 5 Dec 2017 (SOC). In the presence of SOC, it is an ideal DSM naturally with the Dirac points locating at Fermi level exactly, and it would transform into WSM phase by introducing external Zeeman field or by magnetic doping with rare-earth atom Sm. It could also tranform into TI state by breaking rotational symmetry. Our studies show that DSM is a cirtical point for topological phase transition, and the conclusion can apply to most of the DSM materials, not limited to the hexagonal material LiAuSe.2

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“…When an electric field E parallel to B is applied at the same time, this chirality valance breaks down, and the system becomes chiral. This is the origin of the chiral anomaly in Weyl semimetals 1 . It is now clear, as it can be seen employing semiclassical arguments for instance, that the chiral anomaly is a consequence of topologically non-trivial geometrical structures (the Berry curvature Ω and the orbital magnetic moment m 2 ) appearing in Weyl and Dirac semimetals.…”

Section: Introductionmentioning

confidence: 90%

Magnetic-field-induced nonlinear optical responses in inversion symmetric Dirac semimetals

Cortijo

2016

Phys. Rev. B

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We show that, under the effect of an external magnetic field, a photogalvanic effect and the generation of second harmonic wave can be induced in inversion-symmetric and time reversal invariant Dirac semimetals and it is linear with the magnetic field. The mechanisms responsible of these non linear optical responses is the magnetochiral effect and the chiral magnetic effect. What makes possible that these two effects give rise to the discussed non linear optical effects is the presence of band bending effects in the dispersion relation in real Dirac semimetals. Some observable consequences of this phenomenon are the appearance of a dc current on the surface of the system when it is irradiated with linearly polarized light or a rotation of the polarization plane of the reflected second harmonic wave.

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The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal

Cited by 1,709 publications

References 9 publications

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

Magnetic-field-induced nonlinear optical responses in inversion symmetric Dirac semimetals

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