Hall effect in 2D systems with hopping transport and strong disorder

TL;DR

This paper compares theoretical models and numerical simulations of the Hall effect in 2D disordered systems with hopping conduction, highlighting the limitations of the optimal triad model in the VRH regime and proposing an empirical law consistent with experiments.

Contribution

It demonstrates the failure of the optimal triad model in the VRH regime and introduces an empirical law for Hall mobility based on numerical data and experiments.

Findings

Percolation theory agrees with simulations in the nearest neighbor hopping regime.

Optimal triad model fails to describe VRH regime results.

Empirical law matches experimental data in 2D quantum dot arrays.

Abstract

We reconsider the theory of Hall effect in the systems with hopping conduction. The purpose of the present study is to compare the percolation approach based on the optimal triad model with numerical simulations and recent experimental results. We show that, in the nearest neighbor hopping regime, the results of the percolation theory agree to the simulation. However, in the variable range hopping (VRH) regime, the optimal triad model fails to describe the numerical results. It is related to the extremely small probability to find the optimal triad of sites in the percolation cluster in the VRH regime. The contribution of these triads to the Hall effect appears to be small. We describe the Hall mobility in the VRH regime with the empirical law obtained from the numerical results. The law is in agreement with our recent experimental data in 2D quantum dot arrays with the hopping transport.