Density of States of a Two Dimensional Electron Gas in High Magnetic Fields

Abstract

We develop a theory for the electronic density of states of a weakly disordered two dimensional electron gas in the presence of a strong external magnetic field oriented normal to the electron layer. The density of states is calculated using the self-consistent Born approximation for the electron-impurity scattering, retaining Landau level coupling in the theory. The electron-impurity scattering potential is calculated in a non-linear screening approximation where scattering and screening self-consistently determine each other. Screening is treated in the random-phase-approximation by retaining the bubble diagrams and the polarizability is obtained by solving the vertex function within the ladder approximation (which is consistent with the self-energy being treated in the single-site approximation). The resultant level broadening and the electronic density of states cannot easily be characterized by a single parameter such as the zero-field mobility which uniquely characterizes the usual short-range approximation extensively used in the literature. We find that the density of states calculated from this non-linear, self-consistent screening theory is, in general, much smoother and flatter, and the Landau level broadening much larger than that implied in the short-range approximation. The density of states depends on the actual impurity distribution (and, not just on the zero-field mobility) in the system and the level broadening and screening are oscillatory function of the chemical potential. We conclude that in many experimental situations the short-range approximation is even qualitatively wrong.