Magnetotunneling spectroscopy is used as a noninvasive and nondestructive probe to produce two-dimensional spatial images of the probability density of an electron confined in a self-assembled semiconductor quantum dot. The technique exploits the effect of the classical Lorentz force on the motion of a tunneling electron and can be regarded as the momentum (k) space analog of scanning tunneling microscopy imaging. The images reveal the elliptical symmetry of the ground state and the characteristic lobes of the higher energy states.

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  μm a quasiballistic transport via the edge states is observed.

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.

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Hall viscosity is a nondissipative response function describing momentum transport in twodimensional (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 observation of Hall viscosity are correlated with predictions.

We report non-local 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.

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Nonlocal resistance is studied in a two-dimensional system with a simultaneous presence of electrons and holes in a 20 nm HgTe quantum well. A large nonlocal electric response is found near the charge neutrality point (CNP) in the presence of a perpendicular magnetic field. We attribute the observed nonlocality to the edge state transport via counter propagating chiral modes similar to the quantum spin Hall effect at zero magnetic field and graphene near Landau filling factor ν = 0 .