Valley Hall Conductivity in Graphene: Effects of Higher-Order Scattering

Abstract

The valley Hall conductivity, having opposite signs between the K and K′ valleys, is calculated in monolayer and bilayer graphenes with nonzero gap in the presence of short-range scatterers within a single-site approximation. In the case of small disorder, the Hall conductivity is quantized into ±e2/2h and ±e2/h in the monolayer and bilayer graphene, respectively, in the gap region, while it is enhanced over the results in the absence of scatterers in the band region. With the increase in the strength of each impurity potential, large asymmetry between the conduction and valence band appears. For scatterers with attractive potential, the disorder parameter is effectively enhanced and reduced in the conduction and valence band, respectively. The behavior is opposite for repulsive scatterers. Effects of skew scattering causing asymmetry in the scattering direction remain small and do not play significant role.