Electron in a magnetic field and two-dimensional point potentials

Abstract

This paper presents a brief review of the electron properties in two-dimensional systems which contain zero-range scatterers and which are subjected to a magnetic field. The electron spectrum is described for a periodic arrangement of point scatterers and rational magnetic flux per unit cell. Delocalized states on the Landau levels are constructed for the case of positional disorder. The electron localization in a one-dimensional disordered set of scatterers is studied. Application to the study of electron transmission through quantum dots and ballistic channels is reviewed.