Magnetic-Field-Induced Relativistic Properties in Type-I and Type-II Weyl Semimetals

Tchoumakov, Sergueï; Civelli, Marcello; Goerbig, M. O.

doi:10.1103/physrevlett.117.086402

Cited by 148 publications

(136 citation statements)

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“…With respect to the 2-band touching (Weyl point), the only effect of the magnetic field is adding the Zeeman term Bσ z to the Hamiltonian (10). It results in a shift of the Weyl point in the z direction, but the gap never opens.…”

Section: -Band Touchingmentioning

confidence: 99%

“…An interesting feature of Weyl semimetals is that they have a monopole charge in the momentum space, which protects the existence of the Weyl points topologically 2 . The type-II Weyl semimetal has attracted much attention recently [3][4][5][6][7][8][9][10][11][12] , which emerges when the Weyl cone is highly tilted so that the Fermi surface consists of a pair of electron-and hole-pockets touching at the Weyl point. It is experimentally realized in MoTe 2 13-17 , LaAlGe 18 , WTe 2 19-22 , TaIrTe 4 23 , PtTe 2 24 and Ta 3 S 2 25 .…”

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confidence: 99%

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Pseudospin- 32 fermions, type-II Weyl semimetals, and critical Weyl semimetals in tricolor cubic lattices

Ezawa

2016

Phys. Rev. B

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Multi-band touchings such as 3-band, 6-band and 8-band touchings together with the emergence of high pseudospin fermions were predicted recently at high-symmetry points in three-dimensional space. In this paper, we propose a simple cubic model whose unit cell contains three atoms. There are 6 bands in the system due to the spin degrees of freedom. The 4-band and 2-band touchings are realized at high-symmetry points, where we derive low-energy theories, demonstrating the emergence of pseudospin-3/2 fermions and Weyl fermions, respectively. Away from the high-symmetry points, we find critical Weyl fermions present exactly at the boundary between the type-I and type-II Weyl fermions. This critical Weyl fermion transforms into the type-I or type-II Weyl fermion once the magnetic field is applied.Dirac, Weyl and Majorana fermions have attracted much attention in condensed matter physics in views of topology and symmetry. They have a 2-band touching with a linear dispersion. Dirac and Weyl fermions emerge in various materials, which are called Dirac and Weyl semimetals 1 . An interesting feature of Weyl semimetals is that they have a monopole charge in the momentum space, which protects the existence of the Weyl points topologically 2 . The type-II Weyl semimetal has attracted much attention recently [3][4][5][6][7][8][9][10][11][12] , which emerges when the Weyl cone is highly tilted so that the Fermi surface consists of a pair of electron-and hole-pockets touching at the Weyl point. It is experimentally realized in MoTe 2 13-17 , LaAlGe 18 , WTe 2 19-22 , TaIrTe 4 23 , PtTe 2 24 and Ta 3 S 2 25 .Very recently, new types of fermions with multi-band touching were proposed based on the symmetry analysis as well as the first-principles calculations, where 3-band 26,27 , 6-band 26 and 8-band 26,28 touchings were reported at highsymmetry points. Especially, it is shown that the 3-band touchings are well described by the fermions carrying the pseudospin 1. Furthermore, the 8-band touching has been proposed in antiperovskites to produce a pseudospin-3/2 fermion 29 . On the other hand, the 4-band touching is yet to be realized although some discussions were given in the supplement of Ref. 26 .In this paper, motivated by these proposals on multiband touchings and fermions carrying higher pseudospins, we present tight-binding models possessing 4-band and 2-band touchings [ Fig.1]. They are realized naturally in a lattice structure with the cubic symmetry where the unit cell contains three atoms [ Fig.2]. We call it a tricolor cubic lattice. First, we derive the low-energy 4-band theory at the high-symmetry points, which is shown to produce pseudospin-3/2 fermions having the angular momenta j = (−3/2, −1/2, 1/2, 3/2). We also show that the bands have monopole charges −3, −1, 1, 3 at these points. Second, the 2-band theory is described by the Weyl fermion. Furthermore, away from the high-symmetry points, we find a critical Weyl fermion, which resides at the exact boundary of the type-I and type-II Weyl fermions. They transform i...

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Section: -Band Touchingmentioning

confidence: 99%

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confidence: 99%

Pseudospin- 32 fermions, type-II Weyl semimetals, and critical Weyl semimetals in tricolor cubic lattices

Ezawa

2016

Phys. Rev. B

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“…This newly proposed type-II WSM phase [5,6], has been experimentally observed in materials such as MoTe2 [7][8][9][10] and LaAlGe [11], and has been predicted to exist in other materials such as diphosphides of Mo and W [12]. Compared to the type I WSM phase, the type II phase exhibits many novel properties such as non-vanishing finite density of states at Fermi level [5] and anomalous chiral Landau levels [13][14][15]. These properties together with the topologically protected Fermi arc surface states, apart from being interesting in fundamental physics, may be useful in the realisation of quantum computation and high efficiency circuitry.…”

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confidence: 99%

Realizing type-II Weyl points in an optical lattice

2017

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The recent discovery of the Lorentz symmetry-violating 'Type II' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed matter systems. However, tuning the exceptional properties of this novel state has remained a challenge. Optical lattices, created using standing laser beams, provide a convenient platform to tune tunnelling parameters continuously in time. In this paper, we propose a generalised two level system exhibiting type II Weyl points that can be realised using ultra-cold atoms in an optical lattice. The system is engineered using a three-dimensional lattice with complex π phase tunnelling amplitudes. Various unique properties of the type II Weyl semimetal such as open Fermi surface, anomalous chirality and topological Fermi arcs can be probed using the proposed optical lattice scheme. Introduction-In-spite of its theoretical proposal as early as 1929 [1], Weyl Fermion, one of the intriguing particles predicted in the development of quantum field theory, has not been observed as an elementary particle. However, these massless particles have been recently detected in condensed matter experiments as low energy collective excitations, or quasi-particles, in a Weyl SemiMetal (WSM) that supports Fermi-arc topological surface states [2-4]. As described by quantum field theory that is intrinsically relativistic, Weyl Fermions are Lorentz covariant. Nevertheless, Lorentz symmetry can be violated in condensed matter systems, resulting in 'type II' Weyl semimetal phase, that has no equivalent in quantum field theory. This newly proposed type-II WSM phase [5,6], has been experimentally observed in materials such as MoTe2 [7][8][9][10] and LaAlGe [11], and has been predicted to exist in other materials such as diphosphides of Mo and W [12]. Compared to the type I WSM phase, the type II phase exhibits many novel properties such as non-vanishing finite density of states at Fermi level [5] and anomalous chiral Landau levels [13][14][15]. These properties together with the topologically protected Fermi arc surface states, apart from being interesting in fundamental physics, may be useful in the realisation of quantum computation and high efficiency circuitry.

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“…Meanwhile, many experiments have made great efforts to characterize type-II Weyl/Dirac semimetals by angle-resolved photoemission spectroscopy [28][29][30]. This nontrivial Fermi surface could lead to an exotic magnetic-optical response [31][32][33] and unconventional magnetic breakdown [34].…”

Section: Introductionmentioning

confidence: 99%

Renormalization group approach to stability of two-dimensional interacting type-II Dirac fermions

2017

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The type-II Weyl/Dirac fermions are a generalization of conventional or type-I Weyl/Dirac fermions, whose conic spectrum is tilted such that the Fermi surface becomes lines in two dimensions, and surface in three dimensions rather than discrete points of the conventional Weyl/Dirac fermions. The mass-independent renormalization group calculations show that the tilting parameter decreases monotonically with respect to the length scale, which leads to a transition from two dimensional type-II Weyl/Dirac fermions to the type-I ones. Because of the non-trivial Fermi surface, a photon gains a finite mass partially via the chiral anomaly, leading to the strong screening effect of the Weyl/Dirac fermions. Consequently, anisotropic type-II Dirac semimetals become stable against the Coulomb interaction. This work provides deep insight into the interplay between the geometry of Fermi surface and the Coulomb interaction.

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Magnetic-Field-Induced Relativistic Properties in Type-I and Type-II Weyl Semimetals

Cited by 148 publications

References 31 publications

Pseudospin- 32 fermions, type-II Weyl semimetals, and critical Weyl semimetals in tricolor cubic lattices

Pseudospin- 32 fermions, type-II Weyl semimetals, and critical Weyl semimetals in tricolor cubic lattices

Realizing type-II Weyl points in an optical lattice

Renormalization group approach to stability of two-dimensional interacting type-II Dirac fermions

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