Berezinskii-Kosterlitz-Thouless transition in Josephson junction arrays

TL;DR

This paper investigates how quantum fluctuations affect the Berezinskii-Kosterlitz-Thouless transition in 2D Josephson junction arrays, revealing a threshold quantum coupling for transition disappearance and reentrant behavior near this threshold.

Contribution

It provides the first detailed phase diagram of the quantum XY model in Josephson junction arrays, identifying a critical quantum coupling and the effects of dissipation on the transition.

Findings

Genuine BKT transition exists up to a critical quantum coupling g*

Reentrant phase stiffness behavior occurs near g* at low temperatures

Dissipation suppresses the reentrant behavior

Abstract

The quantum XY model shows a Berezinskii-Kosterlitz-Thouless (BKT) transition between a phase with quasi long-range order and a disordered one, like the corresponding classical model. The effect of the quantum fluctuations is to weaken the transition and eventually to destroy it. However, in this respect the mechanism of disappearance of the transition is not yet clear. In this work we address the problem of the quenching of the BKT in the quantum XY model in the region of small temperature and high quantum coupling. In particular, we study the phase diagram of a 2D Josephson junction array, that is one of the best experimental realizations of a quantum XY model. A genuine BKT transition is found up to a threshold value $g^\star$ of the quantum coupling, beyond which no phase coherence is established. Slightly below $g^\star$ the phase stiffness shows a reentrant behavior at lowest temperatures, driven by strong nonlinear quantum fluctuations. Such a reentrance is removed if the dissipation effect of shunt resistors is included.