Thermal transport in a granular metal array

Reliable evaluation of the lattice thermal conductivity is of importance for optimizing the figure-of-merit of thermoelectric materials. Traditionally, when deriving the phonon mediated thermal conductivity $\kappa_{ph} = \kappa - \kappa_{el}$ from the measured total thermal conductivity $\kappa$ the constant Lorenz number $L_0$ of the Wiedemann-Franz law \mbox{$\mathbf{\kappa_{el}}=T L_0 \sigma$} is chosen. The present study demonstrates that this procedure is not reliable w...

We investigate the suppression of the superconducting transition temperature due to Coulomb repulsion in granular metallic systems at large tunneling conductance between the grains, $g_{T}\gg 1$. We find the correction to the superconducting transition temperature for 3$D$ granular samples and films. We demonstrate that depending on the parameters of superconducting grains, the corresponding granular samples can be divided into two groups: (i) the granular samples that belong...

We calculate the Hall conductivity $\sig_{xy}$ and resistivity $\rho_{xy}$ of a granular system at large tunneling conductance $g_{T}\gg 1$. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the gra...

The low-temperature equilibrial state of a system of small metal grains, embedded into insulator, is studied. We find, that the grains may be charged due to the fluctuations of the surface energy of electron gas in grains, rather than quantization of electron states. The higherst-occupied level in a grain fluctuates within the range of order of charging energy below the overall chemical potential. The system, called a gapless Hubbard insulator, has no overall energy gap, whil...

We consider the singular electron-electron interaction corrections to the transport coefficients in disordered metals to test the validity of the Wiedemann-Franz law. We develop a local, quantum kinetic equation approach in which the charge and energy conservation laws are explicitly obeyed. To obtain the local description, we introduce bosonic distribution functions for the neutral, low-energy collective modes (electron-hole pairs). The resulting system of kinetic equations ...

We study the thermal conductivity of the disordered two-dimensional electron gas. To this end we analyze the heat density-heat density correlation function concentrating on the scattering processes induced by the Coulomb interaction in the sub-temperature energy range. These scattering processes are at the origin of logarithmic corrections violating the Wiedemann-Franz law. Special care is devoted to the definition of the heat density in the presence of the long-range Coulomb...

Tunnel transport processes are considered in a square lattice of metallic nanogranules embedded into insulating host to model tunnel conduction in real metal/insulator granular layers. Based on a simple model with three possible charging states ($\pm$, or 0) of a granule and three kinetic processes (creation or recombination of a $\pm$ pair, and charge transfer) between neighbor granules, the mean-field kinetic theory is developed. It describes the interplay between charging ...

A granular metal is an array of metallic nano-particles imbedded into an insulating matrix. Tuning the intergranular coupling strength a granular system can be transformed into either a good metal or an insulator and, in case of superconducting particles, experience superconductor-insulator transition. The ease of adjusting electronic properties of granular metals makes them most suitable for fundamental studies of disordered solids and assures them a fundamental role for nan...

Thermoelectric devices are heat engines, which operate as generators or refrigerators using the conduction electrons as a working fluid. The thermoelectric heat-to-work conversion efficiency has always been typically quite low, but much effort continues to be devoted to the design of new materials boasting improved transport properties that would make them of the electron crystal-phonon glass type of systems. On the other hand, there are comparatively few studies where a prop...

We investigate the effect of Coulomb interactions on the tunneling density of states (DOS) of granular metallic systems at the onset of Coulomb blockade regime in two and three dimensions. Using the renormalization group technique we derive the analytical expressions for the DOS as a function of temperature $T$ and energy $\epsilon$. We show that samples with the bare intergranular tunneling conductance $g^0_{\scriptscriptstyle T}$ less than the critical value $g_{\scriptscri...