Equilibrial Charge of Grains and Low-temperature Conductivity of Granular Metals

The low-temperature equilibrial state of a system of small metal grains, embedded into insulator, is studied. We find, that the grains may be charged due to the fluctuations of the surface energy of electron gas in grains, rather than quantization of electron states. The higherst-occupied level in a grain fluctuates within the range of order of charging energy below the overall chemical potential. The system, called a gapless Hubbard insulator, has no overall energy gap, while the transfer of an electron on finite distances costs finite energy. The ionization energy is determined mostly by the intragrain Coulomb repulsion, rather than a weak intergrain interaction, responsible for the Coulomb gap. The hopping transport in the system is studied. The hopping energy is determined by the charging energy. At low temperature the transport has gapless character.