Critical relations in symmetric $0-\pi$ Josephson junctions

TL;DR

This paper models the critical current behavior of symmetric 0-pi Josephson junctions under magnetic fields, revealing vortex structures and matching experimental data through numerical analysis.

Contribution

It introduces a numerical approach reducing the problem to a non-linear eigenvalue problem and analyzes vortex structures in symmetric 0-pi Josephson junctions.

Findings

Critical current curves are obtained as envelopes of bifurcation curves.

Vortex structures depend on junction length.

Numerical results align well with experimental data.

Abstract

Numerical modeling of dependences ``critical current -- external magnetic field'' for geometrically symmetric $0-\pi$ Josephson junctions is performed. The calculation of critical current is reduced to non-linear eigenvalue problem. The critical curve of the contact is obtained as an envelope of the bifurcation curves of different distributions of the magnetic flux. The structure of vortices in contact is observed explicitly and the dependence of the basic physical characteristics of these vortices on junction's length is explored. The comparison of numerical results and known experimental data shows good qualitative and quantitative conformity.