Variable-range cotunneling and conductivity of a granular metal

The Efros-Shklovskii (E-S) law for the conductivity of granular metals is interpreted as a result of a variable-range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T ≤ T c , while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T ≥ T c . The corresponding E-S temperature T ES , in the latter case, is slightly (logarithmically) T dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T ≪ T c , while, at T > T c , it is suppressed due to inelastic processes, which destroy the interference.