Dirac fermion duality and the parity anomaly

We present a derivation of the recently discovered duality between the free massless (2+1)-dimensional Dirac fermion and QED$_3$. Our derivation is based on a regularized lattice model of the Dirac fermion and is similar to the more familiar derivation of the boson-vortex duality. It also highlights the important role played by the parity anomaly, which is somewhat less obvious in other discussions of this duality in the literature.Comment: 5 pages, typo correcte

Dynamical density response and optical conductivity in topological metals

Topological metals continue to attract attention as novel gapless states of matter. While there by now exists an exhaustive classification of possible topologically nontrivial metallic states, their observable properties, that follow from the electronic structure topology, are less well understood. Here we present a study of the electromagnetic response of three-dimensional topological metals with Weyl or Dirac nodes in the spectrum, which systematizes and extends earlier pioneering studies. In particular, we argue that a smoking-gun feature of the chiral anomaly in topological metals is the existence of propagating chiral density modes even in the regime of weak magnetic fields. We also demonstrate that the optical conductivity of such metals exhibits an extra peak, which exists on top of the standard metallic Drude peak. The spectral weight of this peak is transferred from high frequencies and its width is proportional to the chiral charge relaxation rate.Comment: 10 pages, 2 figures, published versio

Giant Planar Hall Effect in Topological Metals

Much excitement has been generated recently by the experimental observation of the chiral anomaly in condensed matter physics. This manifests as strong negative longitudinal magnetoresistance and has so far been clearly observed in Na$_3$Bi, ZrTe$_5$, and GdPtBi. In this work we point out that the chiral anomaly must lead to another effect in topological metals, that has been overlooked so far: Giant Planar Hall Effect (GPHE), which is the appearance of a large transverse voltage when the in plane magnetic field is not aligned with the current. Moreover, we demonstrate that the GPHE is closely related to the angular narrowing of the negative longitudinal magnetoresistance signal, observed experimentally.Comment: 5 pages, 2 figures, published versio

Mirror Anomaly in Dirac Semimetals

We demonstrate that, apart from the chiral anomaly, Dirac semimetals possess another quantum anomaly, which we call the mirror anomaly, and which manifests in a singular response of the Dirac semimetal to an applied magnetic field. Namely, the anomalous Hall conductivity exhibits step-function singularities when the field is rotated. We show that this phenomenon is closely analogous to the parity anomaly of (2+1)-dimensional Dirac fermions, but with mirror symmetry, which we demonstrate emerges near any Dirac point at a time reversal invariant momentum, replacing the parity symmetry.Comment: 5 pages, 3 figures. Typos corrected. Published versio

Weyl Metals

Weyl metal is the first example of a conducting material with a nontrivial electronic structure topology, making it distinct from an ordinary metal. Unlike in insulators, the nontrivial topology is not related to invariants, associated with completely filled bands, but with ones, associated with the Fermi surface. The Fermi surface of a topological metal consists of disconnected sheets, each enclosing a Weyl node, which is a point of contact between two nondegenerate bands. Such a point contact acts as a source of Berry curvature, or a magnetic monopole in momentum space. Its charge, or the flux of the Berry curvature through the enclosing Fermi surface sheet, is a topological invariant. We review the current state of this rapidly growing field, with a focus on bulk transport phenomena in topological metals.Comment: 21 pages, 6 figures. Review article, submitted to Annual Reviews of Condensed Matter Physics. Added references and fixed a formatting proble

Chiral anomaly and transport in Weyl metals

We present an overview of our recent work on transport phenomena in Weyl metals, which may be connected to their nontrivial topological properties, particularly to chiral anomaly. We argue that there are two basic phenomena, which are related to chiral anomaly in Weyl metals: Anomalous Hall Effect (AHE) and Chiral Magnetic Effect (CME). While AHE is in principle present in any ferromagnetic metal, we demonstrate that a magnetic 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. In other words, a ferromagnetic Weyl metal may be thought of as the only example of a ferromagnetic metal with a purely intrinsic AHE. We further develop a fully microscopic theory of diffusive magnetotransport in Weyl metals. We derive coupled diffusion equations for the total and axial (i.e. node-antisymmetric) charge densities and show that chiral anomaly manifests as a magnetic-field-induced coupling between them. We demonstrate that an experimentally-observable consequence of CME in magnetotransport in Weyl metals is a quadratic negative magnetoresistance, which will dominate all other contributions to magnetoresistance under certain conditions and may be regarded as a smoking-gun transport characteristic, unique to Weyl metals.Comment: 35 pages, 7 figures. Topical review of our recent work on transport in Weyl metal

Negative longitudinal magnetoresistance in Dirac and Weyl metals

It has recently been found that Dirac and Weyl metals are characterized by an unusual weak-field longitudinal magnetoresistance: large, negative, and quadratic in the magnetic field. This has been shown to arise from chiral anomaly, i.e. nonconservation of the chiral charge in the presence of external electric and magnetic fields, oriented collinearly. In this paper we report on a theory of this effect in both Dirac and Weyl metals. We demonstrate that this phenomenon contains two important ingredients. One is the magnetic-field-induced coupling between the chiral and the total (or vector, in relativistic field theory terminology) charge densities. This arises from the Berry curvature and is present in principle whenever the Berry curvature is nonzero, i.e. is nonspecific to Dirac and Weyl metals. This coupling, however, leads to a large negative quadratic magnetoresistance only when the second ingredient is present, namely when the chiral charge density is a nearly conserved quantity with a long relaxation time. This property is specific to Dirac and Weyl metals and is realized only when the Fermi energy is close to Dirac or Weyl nodes, expressing an important low-energy property of these materials, emergent chiral symmetry.Comment: 12+ pages, 1 figure, published versio

Topological response in ferromagnets

We present a theory of the intrinsic anomalous Hall effect in a model of a doped Weyl semimetal, which serves here as the simplest toy model of a generic three-dimensional metallic ferromagnet with Weyl nodes in the electronic structure. We analytically evaluate the anomalous Hall conductivity as a function of doping, which allows us to explicitly separate the Fermi surface and non Fermi surface contributions to the Hall conductivity by carefully evaluating the zero frequency and zero wavevector limits of the corresponding response function. We show that this separation agrees with the one suggested a long time ago in the context of the quantum Hall effect by Streda.Comment: 6 pages, 2 figures, published versio

Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals

We present a microscopic theory of diffusive magnetotransport in Weyl metals and clarify its relation to chiral anomaly. We derive coupled diffusion equations for the total and axial charge densities and show that chiral anomaly manifests as a magnetic-field-induced coupling between them. We demonstrate that a universal experimentally-observable consequence of this coupling in magnetotransport in Weyl metals is a quadratic negative magnetoresistance, which will dominate all other contributions to magnetoresistance under certain conditions.Comment: 5 pages, no figures, published versio

Topological response in Weyl semimetals and the chiral anomaly

We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semi-quantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a $\theta$-term in the action for the electromagnetic field, where $\theta$ is not a constant parameter, like e.g. in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that the $\theta$-term and the corresponding topological response survive for sufficiently weak translational symmetry breaking perturbations, which open a gap in the spectrum of the Weyl semimetal, eliminating the Weyl nodes.Comment: 9 pages, 1 figure, published versio