Influence of dimensionality and statistics on the Coulomb coupling between electron gases or electron-and-hole gases

Abstract

Mutual Coulomb scattering between a one-dimensional electron gas (1DEG) and an i-dimensional electron gas (i=1,2,3), separated by a finite distance l, or a one-dimensional hole gas is considered. The gases can have the same or different statistics. The momentum and energy relaxation frequencies are evaluated using a drifted Fermi-Dirac distribution function and taking into account dynamical screening. For a degenerate 1DEG the main contribution to these frequencies comes from processes involving small momentum changes and backscattering. The screening of the first process can be significant even for a weakly nonideal 1DEG. The contribution of backscattering vanishes at large separations l. The phase-space restrictons imposed by the conservation laws render the scattering rate between two strongly degenerate 1DEG’s exponentially small everywhere except for narrow ranges of the concentrations. The dependences of the scattering rates on the temperature, the carrier concentrations, and the distance l are evaluated analytically and numerically for a number of realistic cases.