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

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.

9 pages, 6 figures; published version with added references and discussion

References in corpus (7)

• Metal-insulator transition in films of doped semiconductor nanocrystals
• Why is the bulk resistivity of topological insulators so small?
• Revealing puddles of electrons and holes in compensated topological insulators
• Theory of hopping conduction in arrays of doped semiconductor nanocrystals
• Density of States and Critical Behavior of the Coulomb Glass
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Cited by in corpus (4)

• Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder
• Hyers-Ulam stability of elliptic Möbius difference equation
• Length scale of puddle formation in compensation-doped semiconductors and topological insulators
• Conductivity of two-dimensional small gap semiconductors and topological insulators in strong Coulomb disorder