Quantum transport in a three-dimensional Weyl electron system

Quantum transport in a three-dimensional Weyl (massless Dirac) electron system with long-range Gaussian impurities is studied theoretically using a self-consistent Born approximation (SCBA). We find that the conductivity significantly changes its behavior at a certain critical disorder strength which separates the weak and strong disorder regimes. In the weak disorder regime, the SCBA conductivity mostly agrees with the Boltzmann conductivity, except for the Weyl point (the band touching point) at which the SCBA conductivity exhibits a sharp dip. In the strong disorder regime, the Boltzmann theory fails in all the energy regions and the conductivity becomes larger the disorder potential increases, contrary to the usual metallic behavior. At the Weyl point, the conductivity and the density of states are exponentially small in the weak disorder regime, and they abruptly rise at the critical disorder strength. The qualitative behavior near zero energy is well described by an approximate analytic solution of the SCBA equation. The theory applies to three-dimensional gapless band structures including Weyl semimetals.