Disorder, screening, and quantum Hall oscillations.

Abstract

The density of states (DOS) of electrons in two-dimensional (2D) quantum wells and the broadening of Landau levels (LL's) is evaluated. The electrons are assumed to interact with screened, charged impurities located at random in the material. The random location of the impurities leads to a disordered environment seen by the electrons. The screening of the impurities by the 2D electron gas is evaluated in a simple Thomas-Fermi model which depends on the DOS at the Fermi surface, n(${E}_{F}$). The DOS and screening are evaluated iteratively at each magnetic field value. We find that the self-consistent evaluation of the DOS and screening leads to broadening of the LL's and n(${E}_{F}$) that oscillates with B. The oscillating LL widths and n(${E}_{F}$) are compared with the data of Heitmann et al., Englert et al., Wang et al., and Smith et al. and reproduce all the observed values quite well. The chief adjustable parameter is the impurity concentration.