Observation of geometry dependent conductivity in two-dimensional electron systems

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.

Determining energy relaxation length scales in two-dimensional electron gases

We present measurements of the energy relaxation length scale $ell$ in two-dimensional electron gases (2DEGs). A temperature gradient is established in the 2DEG by means of a heating current, and then the elevated electron temperature $T_e$ is estimated by measuring the resultant thermovoltage signal across a pair of deferentially biased bar-gates. We adapt a model by Rojek and K{o}nig [Phys. Rev. B textbf{90}, 115403 (2014)] to analyse the thermovoltage signal and as a result extract $ell$, $T_e$, and the power-law exponent $alpha_i$ for inelastic scattering events in the 2DEG. We show that in high-mobility 2DEGs, $ell$ can attain macroscopic values of several hundred microns, but decreases rapidly as the carrier density $n$ is decreased. Our work demonstrates a versatile low-temperature thermometry scheme, and the results provide important insights into heat transport mechanisms in low-dimensional systems and nanostructures. These insights will be vital for practical design considerations of future nanoelectronic circuits.