# Cotunnelling and polaronic effect in granular systems

## TL;DR

This paper presents a theoretical study of conductivity in granular metallic systems, highlighting how polaronic effects due to stray charges influence the transition from variable-range hopping to Arrhenius-like behavior at low temperatures.

## Contribution

It introduces a unified theoretical framework that accounts for both weak and strong polaron effects and describes the crossover from elastic to inelastic cotunneling in granular metals.

## Key findings

- Polaronic effects induce Arrhenius-like conductivity at low temperatures.
- Effective activation energy depends logarithmically on temperature.
- The theory covers both weak and strong polaron regimes and elastic-inelastic cotunneling crossover.

## Abstract

We theoretically study the conductivity in arrays of metallic grains due to the variable-range multiple cotunneling of electrons with short-range (screened) Coulomb interaction. The system is supposed to be coupled to random stray charges in the dielectric matrix that are only loosely bounded to their spatial positions by elastic forces. The flexibility of the stray charges gives rise to a polaronic effect, which leads to the onset of Arrhenius-like conductivity behavior at low temperatures, replacing conventional Mott variable-range hopping. The effective activation energy logarithmically depends on temperature due to fluctuations of the polaron barrier heights. We present the unified theory that covers both weak and strong polaron effect regimes of hopping in granular metals and describes the crossover from elastic to inelastic cotunneling.