Existence and stability analysis of finite 0-$\pi$-0 Josephson junctions

TL;DR

This paper analyzes the existence and stability of semifluxons in finite 0-$$-0 Josephson junctions using analytical and numerical methods, revealing how system parameters influence semifluxon formation and stability.

Contribution

It provides a combined analytical and numerical study of semifluxon stability in finite 0-$$-0 Josephson junctions, highlighting the effects of junction length and bias current.

Findings

Existence of an instability region with spontaneous semifluxon generation.

Dependence of semifluxon existence on junction length, facet length, and bias current.

Numerical simulations confirm analytical predictions.

Abstract

We investigate analytically and numerically a Josephson junction on finite domain with two $\pi$-discontinuity points characterized by a jump of $\pi$ in the phase difference of the junction, i.e. a 0-$\pi$-0 Josephson junction. The system is described by a modified sine-Gordon equation. We show that there is an instability region in which semifluxons will be spontaneously generated. Using a Hamiltonian energy characterization, it is shown how the existence of static semifluxons depends on the length of the junction, the facet length, and the applied bias current. The critical eigenvalue of the semifluxons is discussed as well. Numerical simulations are presented, accompanying our analytical results.