Observation of geometry dependent conductivity in two-dimensional electron systems

Abstract

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 consistent 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.

References in corpus (8)

• Anderson Transitions
• Direct measurement of the phase coherence length in a GaAs/GaAlAs square network
• Many body localization and delocalization in the two dimensional continuum
• Magnetotransport in disordered delta-doped heterostructures
• Low-Temperature Collapse of Electron Localisation in Two Dimensions
• Magnetic field induced Coulomb blockade in small disordered delta-doped heterostructures
• Density-dependent thermopower oscillations in mesoscopic two-dimensional electron gases
• 'Metal'-like transport in high-resistance, high aspect ratio two-dimensional electron gases

Cited by in corpus (3)

• Thermoelectric and electrical transport in mesoscopic two-dimensional electron gases
• Flicker Noise in Two-Dimensional Electron Gas
• A Self-Organized Model for the Flicker Noise in Interacting Two-Dimensional Electron Gas