Magnetic breakdown of a two-dimensional electron gas in a periodic potential

We have measured the magnetoresistance of a two-dimensional electron gas subjected to a one-dimensional periodic potential using structures with periods 150, 300, and 500 nm. In all structures we observe a low-field positive magnetotresistance, which extends up to a critical field at which a new form of magnetic breakdown occurs. This critical field is found to be inversely proportional to the period of the potential, in agreement with a model based on the semiclassical dynamics of electrons. In addition, we have developed a quantum-mechanical formulation of this problem in which the electron streaming, which generates the positive magnetoresistance, arises from the quasibound states of the combined magnetic and periodic potentials. The tunneling coefficient of these states is calculated and found to be small in the limit where ${\mathit{h}}^2$/2${\mathit{ma}}^2$, the kinetic energy of electrons with a wavelength equal to a, the period of the potential, is much less than the amplitude of the potential, as is the case experimentally. The motion of the electrons can then be treated semiclassically.