Quantum electronic transport in semiconductors using the Wigner distribution from first principles.

Electronic transport properties of semiconductors with small band gaps are often not well described by semiclassical methods, because of missing interband interactions between carriers in the valence and conduction bands. We develop a new first-principles formalism based on the Wigner transform to generalize semiclassical transport models to include quantum effects. We apply the method to Bi$_2$Se$_3$, showing that bulk transport properties at low doping concentrations are dominated by the Zener effect, a mechanism in which carriers transfer charge by tunnelling across the band gap. Surprisingly, Zener tunneling occurs also between band subvalleys of energy much larger than the bandgap.