Weyl semimetals are 3D materials with a unique type of spectrum featuring isolated nodal points in the momentum space. To a certain extent, they can be regarded as solid-state matter hosting massless relativistic fermions. In this respect Weyl semimetals bear some analogy with 2D graphene. A minimal model of a Weyl semimetal implies two Weyl points of opposite chirality within the Brillouin zone with a Hamiltonian breaking time-reversal symmetry. Weyl semimetals bear two very specific topological properties. First, the Weyl points are topologically protected against small perturbations as long as they maintain a finite distance in the momentum space. Second, presence of the Weyl points in the bulk spectrum inevitably leads to the appearance of soft Fermi arc excitations on the 2D surface. With increasing concentration of carriers, a Weyl semimetal develops finite Fermi surfaces around each Weyl point. When chemical potential exceeds a certain threshold value, these Fermi surfaces fuse via a Lifshits transition.

We study the Hall response of the Weyl semimetal. Hall conductivity appears due to inherent breaking of time-reversal symmetry and is fully analogous to anomalous Hall effect in ferromagnets with strong spin-orbit coupling. In the case of Weyl semimetals, both bulk states originating in the vicinity of Weyl points and surface Fermi-arc states contribute to the Hall conductivity. We consider both contributions as a function of energy both below and above Lifshits transition. In addition we find that very special disorder effects related to scattering on closely positioned pairs of impurities provide a significant contribution to the Hall conductivity.