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 (TI), 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 bandstructure. This Weyl semimetal has a finite anomalous Hall conductivity, 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.

We present a study of "nodal semimetal" phases, in which non-degenerate conduction and valence bands touch at points (the "Weyl semimetal") or lines (the "line node semimetal") in threedimensional 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 conductivity of the Weyl semimetal, and similarities to the conductivity of graphene in the line node case.

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

Topological semimetals and metals have emerged as a new frontier in the field of quantum materials. Novel macroscopic quantum phenomena they exhibit are not only of fundamental interest, but may hold some potential for technological applications.The study of the electronic structure topology of crystalline materials has emerged in the last decade as a major new theme in the modern condensed matter physics. The starting impetus came from the remarkable discovery of topological insulators, 1,2 but the focus has recently shifted towards topological semimetals and even metals. While the idea that metals can have a topologically nontrivial electronic structure is not entirely new and some of the recent developments were anticipated in earlier work, 3-5 this shift was precipitated by the theoretical discovery of Weyl 6-12 and later Dirac semimetals. [13][14][15] The experimental realization of both Weyl and Dirac semimetals [16][17][18][19][20] within the last couple of years has brought the field to the forefront of quantum condensed matter research.