Quantum Phase Transitions in Josephson Junction Chains

TL;DR

This paper studies quantum phase transitions in a one-dimensional chain of superconducting grains, revealing how junction capacitance influences the superconductor-insulator transition and the persistence of insulating phases.

Contribution

It introduces a model considering both self- and junction capacitances, showing how junction capacitance affects vortex interactions and phase transitions.

Findings

Junction capacitance induces anisotropy in vortex interactions.

Superconductor-insulator transition follows Berezinskii-Kosterlitz-Thouless behavior.

Insulator phase persists even with large junction capacitance.

Abstract

We investigate the quantum phase transition in a one-dimensional chain of ultra-small superconducting grains, considering both the self- and junction capacitances. At zero temperature, the system is transformed into a two-dimensional system of classical vortices, where the junction capacitance introduces anisotropy in the interaction between vortices. This leads to the superconductor-insulator transition of the Berezinskii-Kosterlitz-Thouless type, as the ratios of the Josephson coupling energy to the charging energies are varied. It is found that the junction capacitance plays a role similar to that of dissipation and tends to suppress quantum fluctuations; nevertheless the insulator region survives even for arbitrarily large values of the junction capacitance.