  We theoretically study the conductivity in arrays of metallic grains due to
the variable-range multiple cotunneling of electrons with short-range
(screened) Coulomb interaction. The system is supposed to be coupled to random
stray charges in the dielectric matrix that are only loosely bounded to their
spatial positions by elastic forces. The flexibility of the stray charges gives
rise to a polaronic effect, which leads to the onset of Arrhenius-like
conductivity behavior at low temperatures, replacing conventional Mott
variable-range hopping. The effective activation energy logarithmically depends
on temperature due to fluctuations of the polaron barrier heights. We present
the unified theory that covers both weak and strong polaron effect regimes of
hopping in granular metals and describes the crossover from elastic to
inelastic cotunneling.
