Observation of geometry-dependent conductivity in two-dimensional electron gases

Dirk Backes, Richard Hall, Michael Pepper, Harvey Beere, David Ritchie, Vijay Narayan

Published 2015-05-13Version 1

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 ($n_s$) we find the behaviour to be consistent with $\sigma \sim L^{\alpha}$, where $L$ is the length of the 2DEG along the direction of transport. Importantly, this scale-dependent behaviour is seen to persist even when $\sigma << e^2/h$, when the 2DEG is expected to be strongly localized. This geometry-dependence is seen to disappear as $T$ and/or $n_s$ is increased, which is suggestive of an `insulator-to-metal' transition. We analyze our results in light of the scaling hypothesis of localization and conclude, remarkably, that the reduction in $\sigma$ is consistent with weak localization. Within this framework, we offer an explanation for the anomalous `metallic' character of ultra low-$\sigma$ mesoscopic 2DEGs first observed by Baenninger et al. [Phys. Rev. Lett. 100, 016805 (2008)].