Analytical analysis of ground states on 0-$\pi$ long Josephson junctions

Abstract

We investigate analytically a long Josephson 0-$\pi$-junction with several 0 and $\pi$ facets which are comparable to the Josephson penetration length ${\lambda }_J$. 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 $\pi$ coupling or (c) the structure of the corresponding sine-Gordon equations and substituting the phase $\pi$-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 $a_c$, 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 $a_c$ (bifurcation point) and present the solutions for different number of facets and the edge facets length. We show that the edge facets may drastically affect the state of the system.

submited to PRB

References in corpus (6)

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• Non-ideal artificial phase discontinuity in long Josephson 0-kappa-junctions
• Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0-kappa-junctions
• Stability of $\pi$ junction configurations in ferromagnet-superconductor heterostructures
• Semifluxon molecule under control
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• Shapiro steps in Josephson junctions with alternating critical current density
• Semifluxons in Superconductivity and Cold Atomic Gases
• Quantum tunneling of a single semifluxon in a 0-pi Josephson junction
• Existence and stability analysis of finite 0-$\pi$-0 Josephson junctions
• Localized mode interactions in 0-pi Josephson junctions