Transition between scattering regimes of 2D electron transport

Abstract

We examine 2D electron transport through a long narrow channel driven by an external electric field in presence of diffusive boundary scattering. At zero temperature, we derive an analytical solution of the transition from ballistic to diffusive transport if we increase the bulk disorder strength. This crossover yields characteristic current density profiles. Furthermore, we illustrate the current density in the transition from ballistic to hydrodynamic transport. This corresponds to the Gurzhi effect in the resistivity. We also study the influence of finite temperature on current densities and average current in this system. In particular, we analyze how a particular scaling law of electron-electron scattering with respect to temperature affects the current along the channel.