Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites

TL;DR

This paper reveals that in compensated semiconductors with strong disorder, low-energy sites self-organize into fractal structures that significantly boost hopping conductivity and extend Efros-Shklovskii behavior to higher temperatures.

Contribution

It demonstrates the spontaneous fractal ordering of low-energy sites in disordered semiconductors and its impact on enhancing hopping conductivity beyond traditional models.

Findings

Fractal dimension of low-energy sites is approximately 2.

Fractal ordering greatly increases hopping conductivity.

Efros-Shklovskii conductivity persists at higher temperatures.

Abstract

Variable-range hopping conductivity has long been understood in terms of a canonical prescription for relating the single-particle density of states to the temperature-dependent conductivity. Here we demonstrate that this prescription breaks down in situations where a large and long-ranged random potential develops. In particular, we examine a canonical model of a completely compensated semiconductor, and we show that at low temperatures hopping proceeds along self-organized, low-dimensional subspaces having fractal dimension $d = 2$. We derive and study numerically the spatial structure of these subspaces, as well as the conductivity and density of states that result from them. One of our prominent findings is that fractal ordering of low energy sites greatly enhances the hopping conductivity, and allows Efros-Shklovskii type conductivity to persist up to unexpectedly high temperatures.