Ground states of one and two fractional vortices in long Josephson 0-kappa-junctions

Abstract

Half integer Josephson vortices in 0-$\pi$-junctions, discussed theoretically and observed experimentally, spontaneously appear at the point where the Josephson phase is $\pi$-discontinuous. The creation of \emph{arbitrary} discontinuities of the Josephson phase has been demonstrated recently. Here we study fractional vortices formed at an arbitrary $\kappa$-discontinuity, discuss their stability and possible ground states. The two stable states are not mirror symmetric. Furthermore, the possible ground states formed at two $\kappa$-discontinuities separated by a distance $a$ are investigated, and the energy and the regions of stability of each ground state are calculated. We also show that the ground states may strongly depend on the distance $a$ between the discontinuities. There is a crossover distance $a_c$ such that for $a<a_c$ and for $a>a_c$ the ground states may be qualitatively different.

arXiv comment7 figures, submitted to PRB In v.2 one figure is added, and refs are updated In v.3 major revision, many issues fixed

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• Non-ideal artificial phase discontinuity in long Josephson 0-kappa-junctions
• Observation of a gel of quantum vortices in a superconductor at very low magnetic fields
• Functional superconductor interfaces from broken time-reversal symmetry
• Theory of fractional vortex escape in a 0-kappa long Josephson junction
• Thermal escape of fractional vortices in long Josephson junctions
• Spectroscopy of a fractional Josephson vortex molecule
• Quantum tunneling of a single semifluxon in a 0-pi Josephson junction
• Existence and stability analysis of finite 0-$\pi$-0 Josephson junctions
• Effect of current injection into thin-film Josephson junctions
• A tunable macroscopic quantum system based on two fractional vortices
• Fractional vorticity, Bogomol'nyi-Prasad-Sommerfield systems and complex structures for the (generalized) spinor Gross-Pitaevskii equations