MAGNETORESISTANCE OF A 2-DIMENSIONAL ELECTRON-GAS IN A SQUARE SUPERLATTICE

A calculation of the conductivity of a two-dimensional electron gas with a weak two-dimensional potential modulation in a perpendicular magnetic field is presented. The modulation leads to the Hof- stadter spectrum with the number of branches equal to the integer p, the number of magnetic fluxes per q cells. Despite the irregularities of the dependence of these numbers on the magnetic field, the resulting measurable values such as conductivity appear to behave quite smoothly. Weiss oscillations in the conductivity were obtained and found to have the same dependence on the magnetic field and electron density as for the one-dimensional modulation case. The conductivity due to transitions between Hofstadter levels is strongly suppressed, leading to oscillations in phase with the density of states at the Fermi level. © 1995 The American Physical Society.