Thermal transport in a granular metal array

TL;DR

This paper derives the thermal conductivity formula for granular metals at low temperatures, revealing different behaviors from electrical conductivity and potential deviations from the Wiedemann-Franz law at strong coupling.

Contribution

It provides a detailed analysis of thermal transport in granular metals using the AES model, highlighting the role of inelastic cotunneling and Coulomb effects.

Findings

Thermal conductivity decreases algebraically with temperature, unlike electrical conductivity.

Inelastic cotunneling contributes to thermal transport at low intergrain conductance.

Possible weak deviation from Wiedemann-Franz law at high intergrain coupling.

Abstract

We obtain the Kubo formula for the electronic thermal conductivity kappa(T) of a granular metal array at low temperatures for the Ambegaokar-Eckern-Schoen (AES) model and study the kinetic and potential contributions in the diamagnetic (local) and paramagnetic (current-current) terms. For small values of dimensionless intergrain tunneling conductance, g << 1, we show that inelastic cotunneling processes contribute to thermal conductivity due to non-cancellation of the diamagnetic and paramagnetic terms, unlike electrical conductivity. We find that the electrical conductivity obeys the Arrhenius law, sigma(T) ~ ge^{-E_c/T}, however kappa(T) decreases only algebraically, kappa(T) \~ g^2 T^3/E_c^2. At large values of intergrain coupling, g >> 1, we find it plausible that the Wiedemann-Franz law weakly deviates from the free-electron theory due to Coulomb effects.