Hydrodynamic and ballistic transport in high-mobility GaAs/AlGaAs heterostructures

The understanding and study of electron transport in semiconductor systems has been the instigation behind the growth of semiconductor electronics industry which has enabled technological developments that are part of our everyday lives. However, most materials exhibit diffusive electron transport where electrons scatter off disorder (impurities, phonons, defects, etc.) inevitably present in the system, and lose their momentum. Advances in material science have led to the discovery of materials which are essentially disorder-free and exhibit exceptionally high mobilities, enabling transport physics beyond diffusive transport. In this work, we explore non-diffusive transport regimes, namely, the ballistic and hydrodynamic regimes in a high-mobility two-dimensional electron system in a GaAs quantum well in a GaAs/AlGaAs heterostructure. The hydrodynamic regime exhibits collective fluid-like behavior of electrons which leads to the formation of current vortices, attributable to the dominance of electron-electron interactions in this regime. The ballistic regime occurs at low temperatures, where electron-electron interactions are weak, constraining the electrons to scatter predominantly against the device boundaries.

To study these non-diffusive regimes, we fabricate mesoscopic devices with multiple point contacts on the heterostructure, and perform variable-temperature (4.1 K to 40 K) zero-field nonlocal resistance measurements at various locations in the device to map the movement of electrons. The experiments, along with interpretation using kinetic simulations, demarcate hydrodynamic and ballistic regimes and establish the dominant role of electron-electron interactions in the hydrodynamic regime. To further understand the role of electron-electron interactions, we perform nonlocal resistance measurements in the presence of magnetic field in transverse magnetic focusing geometries under variable temperature (0.39 K to 36 K). Using our experimental results and insights from the kinetic simulations, we quantify electron-electron scattering length, while also highlighting the importance of electron-electron interactions even in ballistic transport. At a more fundamental level, we reveal the presence of current vortices in both hydrodynamic and surprisingly, ballistic regimes both in the presence and absence of magnetic field. We demonstrate that even the ballistic regime can manifest negative nonlocal resistances which should not be considered as the hallmark signature of hydrodynamic regime. The work sheds a new light on both hydrodynamic and ballistic transport in high-mobility solid-state systems, highlighting the similarities between these non-diffusive regimes and at the same time providing a way of effectively demarcating them using innovative device design, measurement schemes and one-to-one modeling. The similarities stem from total electron system momentum conservation in both the hydrodynamic and ballistic regimes. The work also presents a sensitive and precise experimental technique for measuring electron-electron scattering length, which is a fundamental quantity in solid-state physics.