Document Type

Article

Publication Date

8-29-2016

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.

Publication Title

Physical Review B

ISSN

2469-9950

Publisher

American Physical Society

Volume

94

Issue

8

First Page

085146-1

Last Page

085146-9

DOI

10.1103/PhysRevB.94.085146

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