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 nonresonant 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. (C) 2005 Pleiades Publishing, Inc.