Weak localization in metallic granular media

We investigate the interference correction to the conductivity of a medium consisting of metallic grains connected by tunnel junctions. Tunneling conductance between the grains, e²gT∕π, is assumed to be large, gT⪢1. We demonstrate that the weak localization correction to conductivity exhibits a crossover at temperature T~gT²δ, where δ is the mean level spacing in a single grain. At the crossover, the phase relaxation time determined by the electron-electron interaction becomes of the order of the dwell time of an electron in a grain. Below the crossover temperature, the granular array behaves as a continuous medium, while above the crossover the weak localization effect is largely a single-junction phenomenon. We elucidate the signatures of the granular structure in the temperature and magnetic field dependence of the weak localization correction.