Transport properties of granular metals at low temperatures

We investigate transport in a granular metallic system at large tunneling conductance between the grains, gT>>1. We show that at low temperatures, T<=gTd, where d is the mean energy level spacing in a single grain, the coherent electron motion at large distances dominates the physics, contrary to the high-temperature (T>gTd) behavior where conductivity is controlled by the scales of the order of the grain size. In three dimensions we predict the metal-insulator transition at the bare tunneling conductance gCT=(1/6[pi])ln(EC/d), where EC is the charging energy of a single grain. Corrections to the density of states of granular metals due to the electron-electron interaction are calculated. Our results compare favorably with the logarithmic dependence of resistivity in the high-Tc cuprate superconductors indicating that these materials may have a granular structure.