Kinetic equation from Landau level basis: Beyond relaxation-time approximation

Abstract

The purpose of this paper is to formulate a kinetic theory describing transport properties of electrons in a uniform magnetic field of arbitrary magnitude. Exposing an electronic system to a constant magnetic field quenches its energy bands into a series of discrete energy levels, known as Landau levels. The Landau-level states, exact solutions of the Schr\"odinger equation in a constant background magnetic field, are natural and suitable basis to use, especially, for the investigation of strong-magnetic-field phenomena. Starting from the Keldysh formalism, we derive the quantum kinetic equation from the Landau-level basis. As an illustration, we apply the kinetic equation to calculate the electrical conductivity of a two-dimensional electron gas exposed to a perpendicular magnetic field.