Duality in two capacitively coupled layered arrays of ultrasmall Josephson junctions

TL;DR

This paper investigates the duality and phase behavior of two capacitively coupled Josephson junction arrays, exploring regimes from semiclassical superfluidity to quantum vortex-driven insulators, with theoretical predictions for experimental verification.

Contribution

It introduces a duality transformation between charged and vortex regimes in coupled arrays, extending understanding of their quantum and classical phase interactions.

Findings

Derived a duality transformation involving a gauge field.

Provided theoretical predictions for critical temperatures.

Analyzed the effects of quantum and classical regimes in coupled arrays.

Abstract

We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on their physical parameter values. The former case is dominated by a Cooper-pair superfluid while the quantum one is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and Mean Field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one in the quantum fluctuations dominated regimes, we derive a duality transformation between the charged and vortex dominated arrays that involve a gauge vector field, which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.