August 1, 2005
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.
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January 31, 2005
We study the Ambegaokar-Eckern-Sch\"{o}n (AES) model for a regular array of metallic grains coupled by tunnel junctions of conductance $g$ and calculate both paramagnetic and diamagnetic terms in the Kubo formula for the conductivity. We find analytically, and confirm by numerical path integral Monte Carlo methods, that for $0<g<4$ the conductivity obeys an Arrhenius law $\sigma(T)\sim\exp[-E^{*}(g)/T]$ with an effective charging energy $E^{*} (g)$ when the temperature is suf...
February 6, 2004
We study the electron thermal transport in granular metals at large tunnel conductance between the grains, $g_T \gg 1$ and not too low a temperature $T > g_T\delta$, where $\delta$ is the mean energy level spacing for a single grain. Taking into account the electron-electron interaction effects we calculate the thermal conductivity and show that the Wiedemann-Franz law is violated for granular metals. We find that interaction effects suppress the thermal conductivity less tha...
January 7, 2006
We study the finite-temperature optical conductivity, sigma(omega,T), of a granular metal using a simple model consisting of a array of spherical metallic grains. It is necessary to include quantum tunneling and Coulomb blockade effects to obtain the correct temperature dependence of sigma(omega, T), and to consider polarization oscillations to obtain the correct frequency dependence. We have therefore generalized the Ambegaokar-Eckern-Schoen (AES) model for granular metals t...
May 12, 2003
We consider thermodynamic and transport properties of a long granular array with strongly connected grains (inter-grain conductance g>>1.) We find that the system exhibits activated behavior of conductance and thermodynamic density of states ~exp(-T*/T) where the gap, T*, is parametrically larger than the energy at which conventional perturbation theory breaks down. The scale T* represents energy needed to create a long single-electron charge soliton propagating through the a...
April 19, 2003
We investigate transport in a granular metallic system at large tunneling conductance between the grains, $g_T\gg 1$. We show that at low temperatures, $T\leq g_T\delta $, where $\delta$ is the single mean energy level spacing in a grain, the coherent electron motion at large distances dominates the physics, contrary to the high temperature ($T>g_T\delta $) behavior where conductivity is controlled by the scales of the order of the grain size. The conductivity of one and two ...
April 19, 2004
We investigate transport in a granular metallic system at large tunneling conductance between the grains. We show that at low temperatures, $T\leq g_T\delta $, where $\delta$ is the single mean energy level spacing in a grain, the coherent electron motion at large distances dominates the physics, contrary to the high temperature ($T > g_T \delta $) behavior where conductivity is controlled by the scales of the order of the grain size. The conductivity of one and two dimension...
February 13, 2003
We consider effects of Coulomb interaction in a granular normal metal at not very low temperatures suppressing weak localization effects. In this limit calculations with the initial electron Hamiltonian are reduced to integrations over a phase variable with an effective action, which can be considered as a bosonization for the granular metal. Conditions of the applicability of the effective action are considered in detail and importance of winding numbers for the phase variab...
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We calculate the thermal conductivity of interacting electrons in disordered metals. In our analysis we point out that the interaction affects thermal transport through two distinct mechanims, associated with quantum interference corrections and energy exchange of the quasi particles with the electromagnetic environment, respectively. The latter is seen to lead to a violation of the Wiedemann-Franz law. Our theory predicts a strong enhancement of the Lorenz ratio $\kappa /\si...
March 29, 2017
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 l...
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In this work we present a detailed study and derivation of the thermopower and thermoelectric coefficient of nano-granular metals at large tunneling conductance between the grains, g_T>> 1. An important criterion for the performance of a thermoelectric device is the thermodynamic figure of merit which is derived using the kinetic coefficients of granular metals. All results are valid at intermediate temperatures, E_c>>T/g_T>\delta, where \delta is the mean energy level spacin...