Local dissipation effects in two-dimensional quantum Josephson junction arrays with magnetic field

Tomasz Polak

Max Planck Institute for the Physics of Complex Systems

We study the quantum phase transitions in two-dimensional arrays of Josephson-couples junctions with short range Josephson couplings (given by the Josephson energy EJ) and the charging energy EC. We map the problem onto the solvable quantum generalization of the spherical model that improves over the mean-field theory method. The arrays are placed on the top of a two-dimensional electron gas separated by an insulator. We include effects of the local dissipation in the presence of an external magnetic flux f=Φ/Φ0 in square lattice for several rational fluxes f=0,1/2,1/3,1/4 and 1/6. We also have examined the T=0 superconducting-insulator phase boundary as function of a dissipation α0 for two different geometry of the lattice: square and triangular. We have found critical value of the dissipation parameter independent on geometry of the lattice and presence magnetic field.