Magnetoresistance oscillations in a periodically modulated two-dimensional electron gas: The magnetic-breakdown approach

A quasiclassical theory for the commensurate (Weiss) oscillations of the magnetoresistance in two-dimensional (2D) conductors with periodic one-dimensional (1D) potential modulation of arbitrary shape and strength is developed within the magnetic-breakdown (MB) approach. The periodic modulation is assumed to be much stronger than a random impurity potential. It produces an artificial Fermi surface (FS) composed of the two open sheets and closed orbits between them. In perpendicular magnetic field dispersive Landau bands develop as a result of the MB between open sheets and closed orbits. A quantum interference at closed orbits causes Landau bandwidth to oscillate periodically in inverse magnetic field producing the Weiss oscillations in magnetoresistance due to the group velocity oscillations. Periodic filling of the Landau bands at the Fermi level gives rise to the band Shubnikov-de Haas (SdH) oscillations. In agreement with experiment, these low-temperature oscillations first increase in amplitude with the increase of the modulation potential strength and then vanish at higher modulation strength giving rise to the positive magnetoresistance. At low fields (usually less than 0.5-1 T) the Weiss oscillations are stronger than the SdH oscillations since they are less damped by temperature and because the SdH oscillations have additional damping factors: the specific MB factor and the Dingle factor. At higher fields the Weiss oscillations interfere with the SdH oscillations. The interference between the Weiss and the SdH oscillations yields the combinational frequencies some of which are "forbidden" from the viewpoint of classical mechanics. The above experimentally observed effects cannot be explained within the standard perturbative model of the Weiss oscillations with the cosinelike modulation potential in which a narrow Landau bandwidth is proportional to the Laguerre polynomials.