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 (2)

• Semi-fluxons in long Josephson 0-pi-junctions
• Ground state and bias current induced rearrangement of semifluxons in 0-pi long Josephson junctions

Cited by in corpus (6)

• Quantum tunneling of semifluxons
• Ground states of one and two fractional vortices in long Josephson 0-kappa-junctions
• Fluxon-semifluxon interaction in an annular long Josephson 0-pi-junction
• Controllable plasma energy bands in a 1D crystal of fractional Josephson vortices
• Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0-kappa-junctions
• Non-ideal artificial phase discontinuity in long Josephson 0-kappa-junctions