We report electrical conductivity $sigma$ measurements on a range of two-dimensional electron gases (2DEGs) of varying linear extent. Intriguingly, at low temperatures ($T$) and low carrier density ($n_{mathrm{s}}$) we find the behavior to be consist
ent with $sigma sim L^{alpha}$, where $L$ is the length of the 2DEG along the direction of transport. Importantly, such scale-dependent behavior is precisely in accordance with the scaling hypothesis of localization~[Abrahams~textit{et al.}, Phys. Rev. Lett. textbf{42}, 673 (1979)] which dictates that in systems where the electronic wave function $xi$ is localized, $sigma$ is not a material-specific parameter, but depends on the system dimensions. From our data we are able to construct the $beta$-function $equiv (h/e^2) d ln sigma / d ln L$ and show this to be strongly consistent with theoretically predicted limiting values. These results suggest, remarkably, that the electrons in the studied 2DEGs preserve phase coherence over lengths $sim~10~mu$m. This suggests the utility of the 2DEGs studied towards applications in quantum information as well as towards fundamental investigations into many-body localized phases.
We present thermal and electrical transport measurements of low-density (10$^{14}$ m$^{-2}$), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We find that even in the supposedly strongly
localised regime, where the electrical resistivity of the system is two orders of magnitude greater than the quantum of resistance $h/e^2$, the thermopower decreases linearly with temperature indicating metallicity. Remarkably, the magnitude of the thermopower exceeds the predicted value in non-interacting metallic 2DESs at similar carrier densities by over two orders of magnitude. Our results indicate a new quantum state and possibly a novel class of itinerant quasiparticles in dilute 2DESs at low temperatures where the Coulomb interaction plays a pivotal role.
We investigate the Nernst effect in a mesoscopic two-dimensional electron system (2DES) at low magnetic fields, before the onset of Landau level quantization. The overall magnitude of the Nernst signal agrees well with semi-classical predictions. We
observe reproducible mesoscopic fluctuations in the signal which diminish significantly with an increase in temperature. We also show that the Nernst effect exhibits an anomalous component which is correlated with an oscillatory Hall effect. This behavior may be able to distinguish between different spin-correlated states in the 2DES.
We report an universal behaviour of hopping transport in strongly interacting mesoscopic two-dimensional electron systems (2DES). In a certain window of background disorder, the resistivity at low perpendicular magnetic fields follows the expected re
lation $rho(B_perp) = rho_{rm{B}}exp(alpha B_perp^2)$. The prefactor $rho_{rm{B}}$ decreases exponentially with increasing electron density but saturates to a finite value at higher densities. Strikingly, this value is found to be universal when expressed in terms of absolute resistance and and shows quantisation at $R_{rm{B}}approx h/e^2$ and $R_{rm{B}}approx 1/2$ $ h/e^2$. We suggest a strongly correlated electronic phase as a possible explanation.
