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.

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

References in corpus (4)

• Dynamics of semifluxons in Nb long Josephson 0-pi junctions
• Semi-fluxons in long Josephson 0-pi-junctions
• Ground state and bias current induced rearrangement of semifluxons in 0-pi long Josephson junctions
• Analytical analysis of ground states on 0-$\pi$ long Josephson junctions

Cited by in corpus (9)

• Quantum tunneling of semifluxons
• Spectroscopy of the fractional vortex eigenfrequency in a long Josephson 0-kappa junction
• Controllable plasma energy bands in a 1D crystal of fractional Josephson vortices
• 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
• Theory of fractional vortex escape in a 0-kappa long Josephson junction
• Thermal escape of fractional vortices in long Josephson junctions
• Effect of current injection into thin-film Josephson junctions
• Fractional vorticity, Bogomol'nyi-Prasad-Sommerfield systems and complex structures for the (generalized) spinor Gross-Pitaevskii equations