Periodic alternating $0,\pi$-junction structures as realization of $\phi$-Josephson junctions

TL;DR

This paper studies a periodic structure of alternating 0- and pi-Josephson junctions, revealing a phase transition to a phi-junction state with unique current-phase relations and magnetic flux properties.

Contribution

It demonstrates the conditions for phase modulation and the emergence of a phi-junction in a periodic 0-pi Josephson structure, including the transition characteristics.

Findings

Phase transition to a modulated state occurs when junction lengths mismatch exceeds a critical value.

The structure's current-phase relation exhibits two maxima and unusual field dependence.

In the modulated state, the phase difference can vary continuously from -pi to pi.

Abstract

We consider the properties of a periodic structure consisting of small alternating 0- and pi- Josephson junctions. We show that depending on the relation between the lengths of the individual junctions, this system can be either in the homogeneous or in the phase-modulated state. The modulated phase appears via a second order phase transition when the mismatch between the lengths of the individual junctions exceeds the critical value. The screening length diverges at the transition point. In the modulated state, the equilibrium phase difference in the structure can take any value from -pi to pi (phi-junction). The current-phase relation in this structure has very unusual shape with two maxima. As a consequence, the field dependence of the critical current in a small structure is very different from the standard Fraunhofer dependence. The Josephson vortex in a long structure carries partial magnetic flux, which is determined by the equilibrium phase.