QUANTUM MAGNETOTRANSPORT OF A PERIODICALLY MODULATED 2-DIMENSIONAL ELECTRON-GAS

The magnetoresistance of two-dimensional electrons in a periodic potential is studied. The Landau levels are broadened by one-dimensional modulation, and are further split into a Hofstadter-like spectrum by two-dimensional modulation. The recently observed Weiss oscillation manifests the oscillatory bandwidth of broadened Landau levels, where the minima appear at the flat-band condition (zero bandwidth) for one-dimensional modulation. However the flat bands seem to give the maxima for two-dimensional modulation. In this paper, the conductivity for both one- and two-dimensional modulations has been obtained analytically. It is shown that the decrease of the scattering conductivity is enhanced by the band splitting, while the band conductivity is reduced significantly. Consequently, the scattering conductivity decreases faster than the increase of the band conductivity as the Landau level is broadened from the flat band. Therefore the total conductivity shows maximum at flat bands, in contrast to the one-dimensional case. Moreover a numerical study has been made by using the Thouless number method. A dramatic difference is observed between one- and two-dimensional modulations. This can be explained in the same way as the result of band splitting.