Superconducting-insulating transition in quantum three-dimensional Josephson junction arrays with magnetic and charge frustration

We study the effect of the competition between Josephson and charging energies on the phase coherence transition in three–dimensional anisotropic network of Josephson-coupled junctions. in the presence of external magnetic flux and charge frustration. To capture the effects of quantum and spatial fluctuations we employ a quantum spherical approximation for the Josephson-junction array Hamiltonian. We examine the $T=0\mathrm{}$ and finite temperature superconductor-insulator phase transitions as functions of a number of control parameters which include self-capitance and junction capacitance, rational magnetic flux, and the charge frustration parameter as well as the lattice anisotropy.