Analysis of ground states of 0−π long Josephson junctions

Abstract

We investigate analytically a long Josephson 0−π junction with several 0 and π facets which are comparable to the Josephson penetration length λJ. Such junctions can be fabricated exploiting (a) the d-wave order-parameter symmetry of cuprate superconductors; (b) the spacial oscillations of the order parameter in superconductor-insulator-ferromagnet-superconductor structures with different thicknesses of ferromagnetic layer to produce 0 or π coupling; or (c) the structure of the corresponding sine-Gordon equations and substituting the phase π discontinuities by the artificial current injectors. We investigate analytically the possible ground states in such a system and show that there is a critical facet length ac, which separates the states with half-integer flux quanta (semifluxons) from the trivial “flat phase state” without magnetic flux. We analyze different branches of the bifurcation diagram, derive a system of transcendental equations which can be effectively solved to find the crossover distance ac (bifurcation point), and present the solutions for different number of facets and the edge facets length.

Source-reported materials — not catalogue approval

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