Imaging electron flow, interference, and interactions in high-mobility two-dimensional electron gases

This thesis investigates spatially-resolved electron transport through high-mobility two-dimensional electron gases (2DEGs) at low-temperature (T ≤ 4.2 K). Scanning gate microscopy (SGM) is used to image electron flow emanating from a quantum point contact (QPC) into a 2DEG, hosted in a GaAs/AlGaAs heterostructure. Two factors important in determining electron trajectories in 2DEGs are researched: disorder and electron-electron scattering. Furthermore, electron interferometry based on the SGM imaging technique is characterized and used to investigate these two factors. GaAs-based 2DEGs have extremely low levels of disorder, with mean free paths ranging from microns to hundreds of microns at low-temperature. Previous SGM experiments showed that disorder, although present at very low levels, still greatly impacts the spatial structure of electron flow on length scales much shorter than the mean free path; disorder causes electrons to flow along narrow branches. By studying samples with mean free paths ranging over an order of magnitude, this thesis shows how varying levels of disorder affect electron flow. Furthermore, this thesis demonstrates that the branches are surprisingly stable to changes in initial conditions of injected electrons. The formation of branched flow previously had been understood classically, but the newly-observed stability to changes in initial conditions requires a quantum-mechanical explanation. Interference of wave-like electrons traveling along different paths causes interference fringes in images of electron flow. One source of electron paths is impurity scattering, and impurity-induced fringes were observed throughout all previous SGM images of electron flow. A technique to determine locations and densities of impurities in 2DEGs using interference fringes is demonstrated. This thesis reports a lack of impurity-induced fringes in samples with mobility higher than those previously imaged. By imaging electron flow in one of the same high-mobility samples at lower temperatures than previously reported (350 mK), interference fringes from a different mechanism are observed. These fringes are due to an interferometer formed between the QPC and SGM tip, similar to an optical Fabry-Pérot interferometer. New, more complex spatial interference patterns are observed close to the QPC. Interference effects and their destruction are used to investigate dephasing. Electron-electron (e-e) interactions are the dominant source of inelastic scattering and dephasing for electrons in clean 2DEGs at low-temperature. The e-e scattering rate is adjusted by injecting electrons above or below the Fermi energy of the 2DEG. At low injection energies, effects specific to e-e scattering in 2D are found: because of the confined phase space compared to 3D, electrons are scattered by small angles. At high injection energies, an unexpected effect is observed: the differential conductance through the system is increased by moving the SGM tip into the electron flow and thereby backscattering current. This effect can be explained by the injected electron beam scattering with a highly non-equilibrium distribution of electrons in a localized region of 2DEG near the QPC. The e-e scattering rate between injected electrons and this non-equilibrium distribution is measured