Electrons in a Random Potential and Strong Magnetic Field: Lowest Landau Level

Abstract

In this review the properties of two-dimensional independent electrons in a strong perpendicular magnetic field and a random potential are considered in the lowest Landau level. For the density of states of point scatterers an exact expression exists. For the d.c. conductivity and the inverse participation ratio series expansions in the Green’s functions are available. They yield an estimate for the d.c. conductivity in the band centre and for the exponent which describes the vanishing of the inverse participation ratio in the band centre.