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The Coulomb interaction between localized electrons is shown to create a 'soft' gap in the density of states near the Fermi level. The new temperature dependence of the hopping DC conductivity is the most important manifestation of the gap. The form of the density of states within the gap is discussed.

A system consisting of randomly distributed metallic and dielectric regions is considered.The metal-non-metal transition takes place when the volume fraction of the metallic phase approaches the percolation threshold. It is shown that the static dielectric constant diverges near the threshold. Critical indexes are introduced which describe the behaviour of the conductivity and the dielectric constant near the threshold as functions of the volume fraction and frequency. The case of non-zero dc conductivity of dielectric regions is considered also. It is shown that all indexes describing the critical behaviour of complex conductivity can be expressed by two indexes which are known from computer and model experiments. The results of computer calculations of Webman et al. are analysed.PaccMoTpeH cnysag, Icorna nepexon ~e~a a n -n k i a n e~~p~~ I I~O H C X O~H T 3a cqeT

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A theory of photo- and dark-band conductivities in semiconductor supercrystals consisting of nanocrystals is developed by assuming scattering by structural defects in the supercrystals. A new proposed mechanism of photoexcitation, which is triggered by an efficient Auger ionization of charged nanocrystals, provides explanation for the measured photocurrent being 2-3 orders of magnitude larger than the dark current. For dark conductivity, the metal-insulator transitions and temperature dependence of mobility in the metal phase are considered.