Existence and stability analysis of finite 0-$\pi$-0 Josephson junctions

Abstract

We investigate analytically and numerically a Josephson junction on finite domain with two $\pi$-discontinuity points characterized by a jump of $\pi$ in the phase difference of the junction, i.e. a 0-$\pi$-0 Josephson junction. The system is described by a modified sine-Gordon equation. We show that there is an instability region in which semifluxons will be spontaneously generated. Using a Hamiltonian energy characterization, it is shown how the existence of static semifluxons depends on the length of the junction, the facet length, and the applied bias current. The critical eigenvalue of the semifluxons is discussed as well. Numerical simulations are presented, accompanying our analytical results.

Submitted

References in corpus (14)

• 0-pi Josephson tunnel junctions with ferromagnetic barrier
• Periodic alternating $0,\pi$-junction structures as realization of $\varphi$-Josephson junctions
• High quality ferromagnetic 0 and pi Josephson tunnel junctions
• Dynamics of semifluxons in Nb long Josephson 0-pi junctions
• Imaging spontaneous currents in superconducting arrays of pi-junctions
• Quantum tunneling of semifluxons
• Ground states of one and two fractional vortices in long Josephson 0-kappa-junctions
• Analytical analysis of ground states on 0-$\pi$ long Josephson junctions
• Spectroscopy of the fractional vortex eigenfrequency in a long Josephson 0-kappa junction
• The 0 and the pi phase Josephson coupling through an insulating barrier with magnetic impurities
• 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
• Semifluxon molecule under control
• Geometric pi Josephson junction in d-wave superconducting thin films