Quantum percolation in granular metals

TL;DR

This paper develops a theory for quantum corrections to conductivity in granular metals with large, randomly distributed tunnel conductances, revealing a percolative metal-insulator transition driven by quantum fluctuations.

Contribution

It introduces a realistic model accounting for large random tunnel conductances and demonstrates the percolative transition using analytic and numerical methods.

Findings

Quantum fluctuations suppress mean conductance more than its standard deviation.

At low energies, conductance distribution broadens, causing strong local fluctuations.

The metal-insulator transition is characterized as a percolative process.

Abstract

Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below bare charging energy scale E_C) suppress the mean conductance \bar{g}(E) much stronger than its standard deviation \sigma(E). At sufficiently low energies E_* any distribution becomes broad, with \sigma(E_*) ~ \bar{g}(E_*), leading to strong local fluctuations of the tunneling density of states. Percolative nature of metal-insulator transition is established by combination of analytic and numerical analysis of the matrix renormalization group equations.