Variable range cotunneling and conductivity of a granular metal

TL;DR

This paper interprets the Efros-Shklovskii law for granular metal conductivity as arising from variable range cotunneling, distinguishing between elastic and inelastic processes at different temperatures and their effects on magnetoresistance.

Contribution

It introduces a new interpretation of the Efros-Shklovskii law based on variable range cotunneling, highlighting the temperature-dependent transition between elastic and inelastic processes.

Findings

Elastic cotunneling dominates at low temperatures, leading to strong negative magnetoresistance.

Inelastic cotunneling occurs at higher temperatures, reducing interference effects.

The Efros-Shklovskii temperature T_ES varies logarithmically with temperature.

Abstract

The Efros-Shklovskii law for the conductivity of granular metals is interpreted as a result of a variable range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T << T_c, while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T > T_c. The corresponding E-S temperature T_ES in the latter case is slightly (logarithmically) T-dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T much below T_c, while at T>T_c it is suppressed due to inelastic processes which destroy the interference.