A. A. Burkov

Weyl Semimetal in a Topological Insulator Multilayer

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its band structure. This Weyl semimetal has a finite anomalous Hall conductivity and chiral edge states and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator. We find that the Weyl semimetal has a nonzero dc conductivity at zero temperature, but Drude weight vanishing as T(2), and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically protected edge states.

Topological nodal semimetals

We present a study of “nodal-semimetal” phases in which nondegenerate conduction and valence bands touch at points (the “Weyl semimetal”) or lines (the “line-node semimetal”) in three-dimensional momentum space. We discuss a general approach to such states by perturbation of the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time-reversal (TR) or inversion symmetry. We give an explicit model realization of both types of states in a NI-TI superlattice structure with broken TR symmetry. Both the Weyl and the line-node semimetals are characterized by topologically protected surface states, although in the line-node case, some additional symmetries must be imposed to retain this topological protection. The edge states have the form of “Fermi arcs” in the case of the Weyl semimetal: these are chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. The chiral character of the edge states leads to a finite Hall conductivity. In contrast, the edge states of the line-node semimetal are “flat bands”: these states are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone, given by the projection of the line node onto the plane of the edge. We discuss unusual transport properties of the nodal semimetals and, in particular, point out quantum critical-like scaling of the dc and optical conductivities of the Weyl semimetal and similarities to the conductivity of graphene in the line-node case.

Topological response in Weyl semimetals and the chiral anomaly

We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semiquantized 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

Spin and charge transport on the surface of a topological insulator.

\ensuremath{\theta}

Chiral anomaly and transport in Weyl metals

term in the action for the electromagnetic field, where

Weyl semimetal with broken time reversal and inversion symmetries

\ensuremath{\theta}

Axion response in Weyl semimetals

is not a constant parameter, like, for example, in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that the

Supersolid order from disorder: hard-core bosons on the triangular lattice

\ensuremath{\theta}

Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals

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.

Theory of spin-charge-coupled transport in a two-dimensional electron gas with Rashba spin-orbit interactions

We derive diffusion equations, which describe spin-charge coupled transport on the helical metal surface of a three-dimensional topological insulator. The main feature of these equations is a large magnitude of the spin-charge coupling, which leads to interesting and observable effects. In particular, we predict a new magnetoresistance effect, which manifests in a non-Ohmic correction to a voltage drop between a ferromagnetic spin-polarized electrode and a nonmagnetic electrode, placed on top of the helical metal. This correction is proportional to the cross product of the spin polarization of the ferromagnetic electrode and the charge current between the two electrodes. We also demonstrate tunability of this effect by applying a gate voltage, which makes it possible to operate the proposed device as a transistor.