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, T≤g_Tδ, where δ 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_Tδ) 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=(1/6π)ln⁡(E_C/δ), 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.