Correlated hopping of many electrons in the impurity band of moderately compensated semiconductors at low temperature is studied. The growth of the electric dipole moment of the n-electron cluster after the adiabatic switch on of the electron-phonon interaction and the external electric field is calculated. One- and two-phonon processes are considered. The theory is based on the following assumptions: one-electron states in the impurity band are strongly localized, the motion of each electron is restricted to the hopping between two impurity sites, the Coulomb interaction between electrons in the cluster is strong, and the deformation potential type coupling to phonons is assumed. It is shown that the exchange of virtual phonons during the hopping events results in the renormalization of the transfer matrix elements. The calculation also reveals an interference effect between the contributions of different electrons to the current.
