Path integral approach to density of states of two-dimensional electron gas with random potential in transverse magnetic field

Abstract

The behavior of the density of states for an electron moving in a two-dimensional Gaussian random potential under the influence of a transverse magnetic field is studied by using the path integral method. After obtaining the expression for the density of states for the first- cumulant approximation which can compare very well with experiments, some results for the first cumulant approximation suggest that the approximate density of states can take on negative values when the energies of the electron are higher. To overcome this, we could consider going to the second-order cumulant approximation. Although the density of states can be obtained for the second-order cumulant approximation, we cannot observe the behavior of the electron because of the difficulties of an exponential part which cannot be performed analytically. However, it can be calculated numerically by the Monte Carlo method.