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

TL;DR

This paper investigates how local dissipation influences quantum phase transitions in two-dimensional Josephson junction arrays under magnetic fields, revealing a critical dissipation value unaffected by lattice geometry or magnetic flux.

Contribution

It introduces a solvable quantum spherical model approach to analyze dissipation effects in Josephson arrays with magnetic flux, improving upon mean-field methods.

Findings

Critical dissipation value is independent of lattice geometry.

Dissipation affects the superconducting-insulator phase boundary.

Magnetic flux influences phase transitions but not the critical dissipation.

Abstract

We study the quantum phase transitions in two-dimensional arrays of Josephson-couples junctions with short range Josephson couplings (given by the Josephson energy) and the charging energy. 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 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 alpha 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.