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

Abstract

We report electrical conductivity σ 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 σ ∼ L^α , where L is the length of the 2DEG along the direction of transport. Importantly, such scale-dependent behaviour is precisely in accord with the scaling hypothesis of localization [Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)] which dictates that in systems where the electronic wavefunction ξ is localized, σ is not a material-specific parameter, but depends on the system dimensions. From our data we are able to construct the ‘β- function’ ≡ (h/e²)d ln σ/d lnL 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 ∼ 10 µm. This suggests the utility of the 2DEGs studied towards applications in quantum information as well as towards fundamental investigations into many-body localized phases.