MAGNETIC BREAKDOWN IN A 2-DIMENSIONAL ELECTRON-GAS SUBJECTED TO A PERIODIC POTENTIAL

We have measured the magnetoresistance of a two dimensional electron gas subjected to a periodic potential. At very low fields we observe a positive magnetoresistance which extends out to a critical field B(crit). At this field a classical form of magnetic breakdown effect occurs. Experimentally we find B(crit) is-proportional-to V/a where V and a are respectively the amplitude and period of the potential. We can account for this behaviour within a semiclassical model of electron dynamics. A quantum mechanical treatment of this problem is presented which is equivalent to the semiclassical model for a > > 50 nm. For a < 50 nm electrons may tunnel through the maxima of the periodic potential and the semiclassical model breaks down.