Integer quantum Hall effect in single-layer graphene with tilted magnetic field

Abstract

Analytical expression for the Hall conductivity sigma(yx) in graphene is derived in more general case, in which magnetic field is not perpendicular to the plane of the sample. The derivations were carried out using Kubo-Greenwood formulism, which is more suitable when the spectrum is discrete. The results are analyzed as a function of the angle between the magnetic field vector and the normal of the graphene plane. Contrary to the previous theoretical studies, we show that the plateau levels are independent of the direction of the magnetic field. The positions of the plateaus, however, depend on the orientation of the magnetic field.