Spectral Boundary of Positive Random Potential in a Strong Magnetic Field

Abstract

We consider the problem of randomly distributed positive delta-function scatterers in a strong magnetic field and study the behavior of density of states close to the spectral boundary at $E=\hbarω_{c}/2$ in both two and three dimensions. Starting from dimensionally reduced expression of Brezin et al. and using the semiclassical approximation we show that the density of states in the Lifshitz tail at small energies is proportio- nal to $e^{f-2}$ in two dimensions and to $\exp(-3.14f\ln(3.14f/πe)/ \sqrt(2me))$ in three dimensions, where $e$ is the energy and $f$ is the density of scatterers in natural units.