Mean Field Theory for Underdamped Josephson Junction Arrays with an Offset Voltage

TL;DR

This paper develops a mean-field phase diagram for underdamped Josephson junction arrays with offset voltage, revealing complex phases including superconducting, insulating, and supersolid states, and discusses experimental relevance.

Contribution

It introduces a zero-temperature mean-field phase diagram for Josephson junction arrays considering offset voltage and charging energies, highlighting novel supersolid phases.

Findings

Periodic phase diagram in offset voltage with diagonal charging energy.

Degenerate states at specific offset voltages enable phase coherence with minimal Josephson coupling.

Existence of insulating lobes and supersolid phases with coexisting charge order and phase coherence.

Abstract

We study a model Hamiltonian for superconductivity in underdamped Josephson 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 energy, and offset voltage, using a simple Hartree-type mean-field approximation. With diagonal charging energy, the calculated phase diagram is periodic in offset voltage, in agreement with previous results. At a special value of this voltage such that states with n and n+1 Cooper pairs per grain are degenerate, only an infinitesimal Josephson coupling is needed to establish long-range phase coherence in this approximation. With both diagonal and nearest-neighbor charging energies, the T = 0 phase diagram has two types of insulating lobes with different kinds of charge order, and two types of superconducting regions. One of these is a ``supersolid'' in which long-range phase coherence coexists with a frozen charge density wave. We briefly discuss connections to previous calculations, and possible relevance to experiments.