Anomalous Hall Effect in Weyl Metals

Abstract

We present a theory of the anomalous Hall effect (AHE) in a doped Weyl semimetal, or Weyl metal, including both intrinsic and extrinsic (impurity scattering) contributions. We demonstrate that a Weyl metal is distinguished from an ordinary ferromagnetic metal by the absence of the extrinsic and the Fermi surface part of the intrinsic contributions to the AHE, as long as the Fermi energy is sufficiently close to the Weyl nodes. The AHE in a Weyl metal is thus shown to be a purely intrinsic, universal property, fully determined by the location of the Weyl nodes in the first Brillouin zone.An exciting recent development in condensed matter physics is the emerging extension of the concepts of nontrivial electronic structure topology, which have long been confined exclusively to insulators, to gapless metallic states. These ideas, pioneered some time ago by Volovik [1], have recently been brought to the forefront of condensed matter research, with specific solid-state realizations of the first topologically-nontrivial metallic state, a Weyl semimetal, proposed [2][3][4][5]. The recent observation of the closely related Dirac semimetals [6][7][8][9][10][11] paves the way for the realization of Weyl semimetals in the near future.The electronic structure of a Weyl semimetal contains points in momentum space, at which two nondegenerate bands touch at the Fermi energy. Such points, called Weyl nodes, can occur generically (but not necessarily at the Fermi energy) in three-dimensional (3D) band structures, as long as either time-reversal (TR) or inversion (I) symmetries are violated, which is needed to create nondegenerate bands, otherwise prohibited by the Kramers theorem. These points are topologically-nontrivial objects, characterized by an integer topological charge, and are monopole sources of the Berry curvature, momentumspace dual of the magnetic field in real space.Apart from the appearance of the Weyl nodes themselves, which is generically possible in 3D, Weyl semimetal requires the Fermi energy to be aligned with the nodes. This situation is not generic, but is a special case of a Weyl metal: a metal is which the Fermi surface is broken up into disjoint pieces, each surrounding, in the simplest case, a single Weyl node (we will assume such individual sheets of the Fermi surface may be characterized by a Chern number, which is equal to the topological charge, enclosed by the Fermi surface sheet). One may then ask the following question: what are, if any, observable consequences of such a topologically-nontrivial character of the Fermi surface of a Weyl metal?The purpose of this paper is to describe one such phenomenon, which is characteristic of a specific subclass of Weyl metals, namely the ferromagnetic (FM) Weyl metals, in which the nodes owe their existence to broken TR [12]. Any FM metal exhibits anomalous Hall effect (AHE), i.e. an antisymmetric contribution to the offdiagonal resistivity, "proportional" to the magnetization rather than to the applied magnetic field. As has been clearly demonstrated in recen...

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

“…For k 0 = 0, the two Weyl points collapse onto each other giving rise to a topologically trivial (i.e with a zero Berry curvature flux) massless degenerate Dirac fermion. The topological nature of a WSM leads to a host of interesting physics, for example Berry curvature induced anomalous transport, namely charge and thermal Hall conductivities [43][44][45][46][47][48] and open Fermi arcs on surfaces 11,[49][50][51][52][53][54][55] . Anomalous transport phenomena, however, have been already known to exist in a variety of systems which possess a non-trivial distribution of the Berry curvature flux 56,57 .…”

Chirality-Dependent Hall Effect in Weyl Semimetals

“…As a consequence, each nontrivial slice contributes an e 2 /h to the Hall conductivity [9-11] producing σ xy = be 2 /πh in the bulk, and also contributes one edge state to the surface forming a surface Fermi arc connecting the two projected Weyl points. Recently, the Weyl points and surface arcs appear to be observed in optical experiments [23][24][25].This progress may herald a flurry of exciting experiments on the appealing transport effects [26][27][28] predicted in WSM, e.g., the chiral magnetic effect [29][30][31][32][33][34][35][36] when b 0 becomes nontrivial in the absence of P symmetry, and the axial magnetic effect [37,38] when τ b, viewed as a gauge field coupling oppositely to the left-and right-handed Weyl fermions, varies spatially.Here we discover a universal effect in lightly-doped WSMs, by examining the semiclassical dynamics of Weyl quasiparticles in the ballistic regime. The presence of Weyl points leads to substantial Berry curvatures.…”

“…This progress may herald a flurry of exciting experiments on the appealing transport effects [26][27][28] predicted in WSM, e.g., the chiral magnetic effect [29][30][31][32][33][34][35][36] when b 0 becomes nontrivial in the absence of P symmetry, and the axial magnetic effect [37,38] when τ b, viewed as a gauge field coupling oppositely to the left-and right-handed Weyl fermions, varies spatially.…”

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

“…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]. Because Weyl points are monopole sources or drains of the Berry curvature of Bloch wave functions in momentum space, a WSM can exhibit an anomalous Hall effect when breaking the time-reversal symmetry (TRS) [17][18][19] or a spin Hall effect [20], as a linear response to an external electric field. Recent theoretical [21][22][23][24][25][26][27][28][29][30] and experimental [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.…”