Equilibrium properties of a Josephson junction ladder with screening effects

TL;DR

This paper investigates the ground state phase diagram of a Josephson junction ladder considering screening effects, revealing complex vortex density patterns and the influence of inductance approximations on phase stability.

Contribution

It provides a detailed analysis of how screening fields and inductance calculations affect the vortex configurations and phase stability in Josephson junction ladders.

Findings

Vortex density forms a Devil's staircase pattern.

Screening fields extend the stability of metastable phases.

Inductance approximation significantly influences phase diagram features.

Abstract

In this paper we calculate the ground state phase diagram of a Josephson Junction ladder when screening field effects are taken into account. We study the ground state configuration as a function of the external field, the penetration depth and the anisotropy of the ladder, using different approximations to the calculation of the induced fields. A series of tongues, characterized by the vortex density $\omega$, is obtained. The vortex density of the ground state, as a function of the external field, is a Devil's staircase, with a plateau for every rational value of $\omega$. The width of each of these steps depends strongly on the approximation made when calculating the inductance effect: if the self-inductance matrix is considered, the $\omega=0$ phase tends to occupy all the diagram as the penetration depth decreases. If, instead, the whole inductance matrix is considered, the width of any step tends to a non-zero value in the limit of very low penetration depth. We have also analyzed the stability of some simple metastable phases: screening fields are shown to enlarge their stability range.