Monte Carlo simulation of diffusion of interacting electrons in lateral surface superlattices

We have studied the temperature dependence of the transport properties of two-dimensional (2D) electrons in a periodic potential, when the electrons interact through an interparticle Coulomb force. This many-body problem is solved numerically, with a molecular-dynamics Monte Carlo technique. The diffusion constant D shows a monotonic increase with temperature T, but the functional dependence is a power-law type D∼Tn rather than a simple activation type. This power-law dependence is due to the effect of the 2D potential giving rise to a spatial transition of an electron from a potential minimum to another equivalent potential minimum, together with an interparticle Coulomb interaction causing friction in the electron motion and hence forming a dressed electron. The result is fit to the previous theory in the context of a particle moving in a periodic potential with a friction force, and the exponent K in the power-law expression shows a consistent potential dependence with the model.