Quantum magnetotransport of a periodically modulated two-dimensional electron gas

Abstract

A quantum mechanical theory is developed for the recently discovered magnetoresistance oscillations in a periodically and weakly modulated two-dimensional electron gas. The bandwidth of the modulation-broadened Landau levels at the Fermi energy oscillates with magnetic field and gives rise to magnetoresistance oscillations parallel (${\rho }_{\mathrm{xx}}$) and perpendicular (${\rho }_{\mathrm{yy}}$) to the modulation. Diffusion current contributions, proportional to the square of the bandwidth, dominate ${\rho }_{\mathrm{xx}}$; collisional ones, which are large for small bandwidths, dominate ${\rho }_{\mathrm{yy}}$. ${\rho }_{\mathrm{yy}}$ and ${\rho }_{\mathrm{xx}}$ oscillate out of phase as observed. New oscillations in the Hall resistance, the cyclotron resonance position, and the linewidth are predicted.