Long time relaxation of interacting electrons in the regime of hopping conduction

TL;DR

This study uses numerical simulations to explain long-term relaxation and aging in hopping conduction by analyzing slow transitions between pseudoground states with varying conductivities, aligning with experimental observations.

Contribution

It demonstrates that long time relaxation can be explained by slow pseudoground state transitions and shows how disorder strength affects this relaxation in two-dimensional models.

Findings

Long time relaxation explained by pseudoground state transitions

Universality of Coulomb gap suppresses relaxation in strong disorder

Dispersion of conductivities matches experimental data

Abstract

Using numerical simulations we studied the long time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation, still we have been able to show that the long time relaxation and aging effect observed in experiments can be explained in terms of slow transitions between different pseudoground states. This was achieved by showing that different pseudoground states may have different conductivities and that the dispersion of conductivities is in agreement with the experimental data. We considered two different two-dimensional models with electron-electron interaction: the lattice model and the random site model, corresponding to ``strong'' and ``weak'' effective disorder. For the lattice model, effectively strong disorder, we have shown that the universality of the Coulomb gap, which is responsible for the universal Efros-Shklovskii law for the conductivity, suppresses the long time relaxation of conductivity since the universality strongly decreases the dispersion of conductivities of the pseudoground states.