Two-dimensional electrons in lateral magnetic superlattices

Abstract

The properties of electrons moving in two dimensions under the influence of a perpendicular magnetic field of arbitrary strength and which is periodic in one direction are investigated. The magnetic-field modulation is such that the average magnetic-field strength is zero. Four different situations are considered: (1) a magnetic Kronig-Penney system in which the magnetic-field profile consists of a periodic array of \ensuremath{\delta} functions with alternating sign, (2) a periodic array of magnetic-field steps, (3) a sinusoidal magnetic field profile, and (4) a saw-tooth magnetic-field profile. In contrast with the usual potential-modulated case, the present systems are not separable and are inherently two dimensional. We found that the energy spectrum consists of magnetic minibands. With the different reigons of the energy spectrum we are able to associate particular classical trajectories of the electrons. The density of states and the different components of the conductivity tensor are calculated and exhibit a rich structure due to the presence of the magnetic minibands.