Critical fields and devil's staircase in superconducting ladders

TL;DR

This paper investigates the ground states of superconducting ladder systems, revealing a devil's staircase pattern in vortex density and analyzing critical fields analytically, highlighting the effects of short-range vortex interactions.

Contribution

It provides the first analytical calculation of critical fields and demonstrates the devil's staircase phenomenon in superconducting ladder arrays.

Findings

Vortex interactions decay exponentially with distance.

Ground state vortex density forms a devil's staircase pattern.

Critical fields depend only on ladder connectivity and plaquette area.

Abstract

We have determined the ground state for both a ladder array of Josephson junctions and a ladder of thin superconducting wires. We find that the repulsive interaction between vortices falls off exponentially with separation. The fact that the interaction is short-range leads to novel phenomena. The ground state vortex density exhibits a complete devil's staircase as the applied magnetic field is increased, each step producing a pair of metal-insulator transitions. The critical fields in the staircase are all calculated analytically and depend only on the connectivity of the ladder and the area of the elementary plaquette. In particular the normal square ladder contains no vortices at all until the flux per plaquette reaches 0.5/sqrt{3} flux quanta.