Magnetic von Neumann lattice for two-dimensional electrons in a magnetic field

Abstract

One-particle eigenstates and eigenvalues of two-dimensional electrons in a strong magnetic field with short-range impurities, cosine potential, boundary potential, and a periodic array of short-range potentials are obtained by use of the magnetic von Neumann lattice in which Landau-level wave functions have minimum spatial extensions. We find that there is a dual correspondence between the cosine potential and the lattice kinetic term and that the representation based on the von Neumann lattice is quite useful for solving the dynamics of the system.