Conductance statistics in small insulating GaAs:Si wires at low temperature. II. Experimental study

TL;DR

This study experimentally investigates conductance fluctuations in small GaAs:Si wires near the Anderson transition at low temperatures, revealing non-ergodic behavior and validating theoretical models of quantum fluctuations and magnetoconductance.

Contribution

It provides the first detailed experimental analysis of conductance statistics and their evolution in small insulating GaAs:Si wires near the Anderson transition, including non-ergodic effects.

Findings

Conductance fluctuations are reproducible and log-normal.

Fluctuations are non-ergodic outside the critical region.

Magnetoconductance saturates in the strongly localized regime.

Abstract

We have observed reproducible conductance fluctuations at low temperature in a small GaAs:Si wire driven across the Anderson transition by the application of a gate voltage. We analyse quantitatively the log-normal conductance statistics in terms of truncated quantum fluctuations. Quantum fluctuations due to small changes of the electron energy (controlled by the gate voltage) cannot develop fully due to identified geometrical fluctuations of the resistor network describing the hopping through the sample. The evolution of the fluctuations versus electron energy and magnetic field shows that the fluctuations are non-ergodic, except in the critical insulating region of the Anderson transition, where the localization length is larger than the distance between Si impurities. The mean magnetoconductance is in good accordance with simulations based on the Forward-Directed-Paths analysis, i.e. it saturates to $ {\rm ln} (\sigma (H>1)/\sigma (0))\simeq 1, $ as $ \sigma (0) $ decreases over orders of magnitude in the strongly localized regime.