Transport Regimes Of Two-Dimensional Electrons In A Channel Geometry

Electron transport in 2D channels is particular because of the restricted phase space. In the regime of ballistic transport, charge carriers travel without scattering until they reach a boundary of the system. Early experiments in the 1990s focused on 2D electron gases in high-mobility semiconductor heterostructures, such as GaAs/AlGaAs quantum wells. Subsequently, genuine 2D materials such as graphene or transition metal dichalcogenides enter the stage. Hydrodynamic transport, on the other hand, emerges when electron-electron scattering dominates, causing charge carriers to flow collectively, similar to a viscous fluid. This regime, which gained significant attention in recent years, has been claimed to be observed in 2D materials like graphene and palladium cobalate. This Thesis examines different transport regimes that occur in a two-dimensional channel geometry. We examine 2D electron transport through a long narrow channel driven by external electric and magnetic fields 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 particular scaling laws of electron-electron scattering with respect to temperature affect the current along the channel. In the case of weak electron-electron scattering, we derive an analytical solution of the current that allows us to better understand its temperature dependence.