We report electrical and magneto transport measurements in mesoscopic size, two-dimensional (2D) electron gas in a GaAs quantum well. Remarkably, we find that the probe configuration and sample geometry strongly affects the temperature evolution of local resistance. We attribute all transport properties to the presence of hydrodynamic effects. Experimental results confirm the theoretically predicted significance of viscous flow in mesoscopic devices.

The transport properties of the ``inverted'' semiconductor HgTe-based quantum well, recently shown to be a two-dimensional topological insulator, are studied experimentally in the diffusive regime. Nonlocal transport measurements are performed in the absence of magnetic field, and a large signal due to the edge states is observed. This shows that the edge states can propagate over a long distance, $\sim${}1 mm, and therefore, there is no difference between local and nonlocal electrical measurements in a topological insulator. In the presence of an in-plane magnetic field a strong decrease of the local resistance and complete suppression of the nonlocal resistance is observed. We attribute this behavior to an in-plane magnetic-field-induced transition from the topological insulator state to a conventional bulk metal state.

Hall viscosity is a nondissipative response function describing momentum transport in two-dimensional (2D) systems with broken time-reversal symmetry. In the classical regime, Hall viscosity contributes to the viscous flow of 2D electrons in the presence of a magnetic field. We observe a pronounced, negative Hall resistivity at low magnetic field in a mesoscopic size, two-dimensional electron system, which is attributed to Hall viscosity in the inhomogeneous charge flow. Experimental results supported by a theoretical analysis confirm that the conditions for the observation of Hall viscosity are correlated with predictions.

We report resistance measurements in HgTe wells with an inverted band structure near the charge neutrality point (CNP), where the system is expected to be a two-dimensional topological insulator with a dominant edge states contribution. The sample resistance is found to be about 100 times higher than the resistance quantum $h/2{e}^{2}$. Surprisingly, instead of a strong temperature dependence expected in such a seemingly insulating state the resistance at the CNP is found to be temperature independent at low temperatures. The experimental results are compared to the recent theoretical models.

Our experimental studies of electron transport in wide (14 nm) HgTe quantum wells confirm the persistence of a two-dimensional topological insulator state reported previously for narrower wells, where it was justified theoretically. Comparison of local and nonlocal resistance measurements indicate edge state transport in the samples of about 1 mm size at temperatures below 1 K. Temperature dependence of the resistances suggests an insulating gap of the order of a few meV. In samples with sizes smaller than $10\mu \mathrm{m}$ a quasiballistic transport via the edge states is observed.

We report nonlocal electrical measurements in a mesoscopic size two-dimensional (2D) electron gas in a GaAs quantum well in a hydrodynamic regime. Viscous electric flow is expected to be dominant when electron-electron collisions occur more often than the impurity or phonon scattering events. We observe a negative nonlocal resistance and attribute it to the formation of whirlpools in the electron flow. We use the different nonlocal transport geometries and compare the results with a theory demonstrating the significance of hydrodynamics in mesoscopic samples.