Feynman path integration of elelectron transport in two dimensions

Abstract

We have studied the formulation of quantum transport problem in the form of Feynman's path integrals. The idea was originated from the study of polaron transportation by Thornber. We have applied this technique to the problem of an electron transport in two-dimensional system with an applied magnetic Ifield in perpendicular direction and weak disorder. This system may be though of the integer quantum Hall system. First, we show that this technique can be used to determine the non-linear transportation in the high field regime and secondly, we determine the transport coefficients in the linear transport regime of our model system. We have calculated the longitudinal and transverse (Hall) conductivities in the case of clean system and a disorder system at the long-correlation length limit. We find that in the case of absence of disorder the longitudinal component vanishes and the transverse component is well stepped. In the case of disorder system the transverse component appear at the plateau-plateau transition regions. The transverse component appear to have plateau regions. The higher level of approximations are discussed and the advantages of this technique are also expressed.