Weyl and Dirac semimetals in three-dimensional solids

Armitage, N. P.; Mele, E. J.; Vishwanath, Ashvin

doi:10.1103/revmodphys.90.015001

Cited by 4,183 publications

(3,695 citation statements)

References 506 publications

(719 reference statements)

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“…(For recent reviews, see Refs. [1][2][3].) The nontrivial topology of Weyl materials is directly related to the Weyl nodes which act as sources of the Berry curvature in the reciprocal space [4] with the corresponding topological charges (n = 1, 2, 3) determined by the crystallographic point symmetries [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

Gorbar¹,

Miransky²,

Shovkovy³

et al. 2017

Phys. Rev. B

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The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and thermal Hall effects in the absence of background magnetic fields. Similarly to the anomalous Hall effect, all anomalous thermoelectric coefficients are proportional to the integer topological charge of the Weyl nodes. The dependence of the thermoelectric coefficients on the chemical potential and temperature is also studied.

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Section: Introductionmentioning

confidence: 99%

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

Gorbar¹,

Miransky²,

Shovkovy³

et al. 2017

Phys. Rev. B

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“…Introduction -The Weyl semimetal (WSM) [1][2][3][4][5][6] is a topological state characterized by linear band crossing points called Weyl points near the Fermi energy. WSM materials such as the TaAs-family pnictides [7,8] and MoTe 2 [9,10] have recently been discovered primarily by observation of the unique Fermi arcs of surface states through angle-resolved photoemission spectroscopy [11][12][13][14][15][16].…”

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confidence: 99%

Berry curvature dipole in Weyl semimetal materials: An ab initio study

2018

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Noncentrosymmetric metals are anticipated to exhibit a dc photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an ab initio scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and MoTe2-family type-II WSMs. Both types of WSMs exhibited a Berry curvature dipole, in which type-II Weyl points are usually superior to the type-I because of the strong tilt. Corresponding nonlinear susceptibilities in several materials promise a nonlinear Hall effect in the dc field limit, which is within the experimentally detectable range. [31][32][33][34] studies have revealed giant nonlinear optical responses in inversion-symmetry-breaking WSMs, such as the photocurrent from the circular photogalvanic effect (CPGE), second harmonic generation (SHG), and nonlinear Hall effect. These nonlinear effects can be much stronger in WSMs than traditional electro-optic materials owing to the large Berry curvature [22,35,36]. Introduction -

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“…Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

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Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

et al. 2017

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Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50]. Despite this diversity, topological semimetals can be further classified and characterized by the dimensionality of their band crossings in the bulk Brillouin zone (BZ). In a Dirac/Weyl semimetal or an unconventional (higher-fold degenerate) fermion semimetal [41,[43][44][45][46], the conduction and valence bands cross at discrete points in the BZ. Therefore, the dimension of their band crossings is 0D. In a nodal-line semimetal [38], the conduction and valence bands touch along a closed loop, thus the dimension of its band crossing is 1D. In this letter, we propose a number of previously unidentified topological semimetals and identify a candidate material class for the experimental realization. They feature 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain enabled by perpendicular mirror planes. The Hopf link, which consists of two rings that pass through the center of each other, represents the simplest topologically nontrivial link. While originally studied in mathematics and other areas, recently, researchers have applied this concept into topological physics in order to construct novel topological insulators and superconductors [52][53][54], although the role of Hopf link is distinctly different from what is considered here. Here we apply this idea in metals and show that the c...

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Weyl and Dirac semimetals in three-dimensional solids

Cited by 4,183 publications

References 506 publications

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

Berry curvature dipole in Weyl semimetal materials: An ab initio study

Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

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