Quantum Transport in Two-Dimensional Graphite System

Abstract

In a self-consistent Born approximation, the density of states and the conductivity are calculated in a two-dimensional graphite sheet in magnetic fields. Two different cases of scatterers are considered, the short-range case where the range is smaller than the lattice constant and the long-range case where it is comparable or slightly larger. The quantum theory provides results quite different from the results of Boltzmann transport theory even in the absence of a magnetic field. In high magnetic fields, the conductivity exhibits a series of peaks, whose values depend only on the natural constants and the Landau level index. The conductivity of undoped systems is always given by a universal conductivity \(e^{2}/\pi^{2}\hbar\) independent of a magnetic field.