Charge-Vortex Duality in Double-Layered Josephson Junction Arrays

TL;DR

This paper explores a duality in double-layer Josephson junction arrays where vortices and charges in different layers influence each other, revealing two Berezinskii-Kosterlitz-Thouless transitions affected by interlayer capacitance.

Contribution

It introduces a charge-vortex duality in coupled Josephson arrays and analyzes how interlayer capacitance influences phase transitions and transition temperatures.

Findings

Two BKT transitions for vortices and charges in the system.

Interlayer capacitance suppresses transition temperatures.

Vortex transition is more robust than charge transition.

Abstract

A system of two parallel Josephson junction arrays coupled by interlayer capacitances is considered in the situation where one layer is in the vortex-dominated and the other in the charge-dominated regime. This system shows a symmetry (duality) of the relevant degrees of freedom, i.e. the vortices in one layer and the charges in the other. In contrast to single-layer arrays both contribute to the kinetic energy. The charges feel the magnetic field created by vortices, and, vice versa, the vortices feel a gauge field created by charges. For long-range interaction of the charges the system exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and another one for charges. The interlayer capacitance suppresses both transition temperatures. The charge-unbinding transition is suppressed already for relatively weak coupling, while the vortex-unbinding transition is more robust. The shift of the transition temperature for vortices is calculated in the quasi-classical approximation for arbitrary relations between the capacitances (both weak and strong coupling).