Origin of dissipative Fermi arc transport in Weyl semimetals

By making use of a low-energy effective model of Weyl semimetals, we show that the Fermi arc transport is dissipative. The origin of the dissipation is the scattering of the surface Fermi arc states into the bulk of the semimetal. It is noticeable that the corresponding scattering rate is nonzero and can be estimated even in a perturbative theory, although in general the reliable calculations of transport properties necessitate a nonperturbative approach. Nondecoupling of the surface and bulk sectors in the low-energy theory of Weyl semimetals invalidates the usual argument of a nondissipative transport due to one-dimensional arc states. This property of Weyl semimetals is in drastic contrast to that of topological insulators, where the decoupling is protected by a gap in the bulk. Within the framework of the linear response theory, we obtain an approximate result for the conductivity due to the Fermi arc states and analyze its dependence on chemical potential, temperature, and other parameters of the model.