MEAN-FIELD THEORY FOR UNDERDAMPED JOSEPHSON-JUNCTION ARRAYS WITH AN OFFSET VOLTAGE

We study a model Hamiltonian for superconductivity in underdamped Jose phson-junction arrays in the presence of an offset voltage between the array and the substrate. We develop an approximate zero-temperature ( T = 0) phase diagram as a function of Josephson coupling, charging ene rgy, and offset voltage, using a simple Hartree-type mean-field approx imation. With diagonal charging energy, the calculated phase diagram i s periodic in offset voltage, in agreement with previous results. At a special value of this voltage such that states with n and n + 1 Coope r pairs per gain are degenerate, only an infinitesimal Josephson coupl ing is needed to establish long-range phase coherence in this approxim ation. With both diagonal and nearest-neighbor charging energies, the T = 0 phase diagram has two types of insulating lobes with different k inds of charge order, and two types of superconducting regions. One of these is a ''supersolid'' in which long-range phase coherence coexist s with a frozen charge-density wave. We briefly discuss connections to previous calculations, and possible relevance to experiments.