Thermal transport in a granular metal array

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.

5 pages RevTeX, to appear in Physical Review Letters

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• Single grain heating due to inelastic cotunneling
• Thermoelectric performance of weakly coupled granular materials
• Optical conductivity of a granular metal at not very low temperatures
• Keldysh field theory of a driven dissipative Mott insulator: nonequilibrium response and phase transitions
• Heating Effects in a Chain of Quantum Dots
• Magnetic field-dependent inhomogeneities and their effect on the magnetoresponse of 2D superconductors