Semiclassical magnetotransport theory for two-dimensional electron systems in lateral superlattices

Based on the correct single-electron energy spectra we calculate, within a semiclassical approach, the conductivity of periodically modulated two-dimensional electron systems in a perpendicular magnetic field B. For B = O we obtain, as a function of the Fermi energy, fluctuations of the conductivity, which result from the energy gaps in a perfectly periodic modulation potential, but may easily be smeared out by disorder. Introducing a smooth interpolation between the energy bands in the extended zone scheme and taking magnetic breakdown effects properly into account, we calculate the magnetoresistance for a strong unidirectional modulation and magnetic fields of arbitrary strengths, neglecting these quantum fluctuations.