Transport properties of granular metals at low temperatures

We investigate transport in a granular metallic system at large tunneling conductance between the grains, g(T)>1. We show that at low temperatures, Tless than or equal tog(T)delta, where delta 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>g(T)delta) 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 g(T)(C)=(1/6pi)ln(E-C/delta), where E-C 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-T-c cuprate superconductors indicating that these materials may have a granular structure.