Effective Boundary Field Theory for a Josephson Junction Chain with a Weak Link

TL;DR

This paper models a Josephson Junction chain with a weak link as a two-boundary Sine-Gordon system, deriving an analytic expression for the Josephson current and identifying a crossover in current behavior indicating a boundary relevance transition.

Contribution

It introduces an effective boundary field theory for a Josephson Junction chain with a weak link, providing analytic results for the Josephson current and revealing a crossover in behavior.

Findings

Analytic expression for DC Josephson current as a function of phase difference.

Identification of a crossover from sinusoidal to sawtooth current behavior.

Transition from irrelevant to relevant boundary operator regime.

Abstract

We show that a finite Josephson Junction (JJ) chain, ending with two bulk superconductors, and with a weak link at its center, may be regarded as a condensed matter realization of a two-boundary Sine-Gordon model. Computing the partition function yields a remarkable analytic expression for the DC Josephson current as a function of the phase difference across the chain. We show that, in a suitable range of the chain parameters, there is a crossover of the DC Josephson current from a sinusoidal to a sawtooth behavior, which signals a transition from a regime where the boundary term is an irrelevant operator to a regime where it becomes relevant.