Weak localization effects in granular metals

TL;DR

This paper calculates the weak localization correction to conductivity in granular metals, showing similarities to disordered metals but with grain-specific parameters, and finds no conducting phase for dimensions two or less.

Contribution

It extends the weak localization correction analysis to granular metals, replacing traditional parameters with grain-specific ones, and explores the effects on magnetoconductivity.

Findings

No conducting phase for dimensions D ≤ 2 at zero temperature.

Weak localization correction similar to disordered metals with grain-specific parameters.

Analysis of magnetoconductivity correction in weak magnetic fields.

Abstract

The weak localization correction to the conductivity of a granular metal is calculated using the diagrammatic technique in the reciprocal grain lattice representation. The properties of this correction are very similar to that one in disordered metal, with the replacement of the electron mean free path $\ell $ by the grain diameter $d$ and the dimensionless conductance $g$ by the tunnelling dimensionless conductance $g_{T}$. In particular, we demonstrate that at zero temperature no conducting phase can exist for dimensions $D\leq 2$. We also analyze the WL correction to magnetoconductivity in the weak field limit.