Anomalous surface conductivity of Weyl semimetals

We calculate the surface dc conductivity of Weyl semimetals and show that it contains an anomalous contribution in addition to a regular, Drude-like contribution from the Fermi arc. The anomalous part is independent of the surface scattering time and appears at nonzero temperature and chemical potential, increasing quadratically with both. It is found that the nontrivial coupling between the surface and the bulk leads to an effective description on the surface that mimics an interacting two-dimensional fluid in certain regimes of energy, even in the absence of any explicit scattering on the surface, and is responsible for the anomalous contribution. Remarkably, in the case of a layered Weyl semimetal, the temperature-dependent part of the surface conductivity is dominated by the anomalous response which can be probed experimentally to unravel this unusual behavior.