Localization of Electrons under Strong Magnetic Fields in a Two-Dimensional System

Abstract

Using an effective Hamiltonian to describe the dynamics of the center coordinates of the cyclotron motion, the structure of the tail states of the Landau subbands is discussed. Eigenvalue problem is explicitly solved in the case of a single Gaussian-type potential. The eigenfunctions do not depend on the range of the potential while the eigenvalues do. The contribution of the tail states to the dynamical conductivity is shown to be proportional to D(E_F)²ω² In ω in the low frequency limit with D(E_F) the density of states at the Fermi energy E_F.