Existence and stability analysis of semifluxons in disk-shaped two-dimensional0−πJosephson junctions

Abstract

We consider a disk-shaped two-dimensional Josephson junction with concentric regions of 0- and $\ensuremath{\pi}$-phase shifts and investigate its ground states. This system is described by a $(2+1)$-dimensional sine-Gordon equation, which becomes effectively one dimensional in polar coordinates when one considers radially symmetric static solutions. We show that there is a parameter region in which the ground state corresponds to a spontaneously created ring-shaped semifluxon. We use a Hamiltonian energy characterization to describe analytically the dependence of the semifluxonlike ground state on the junction size and the applied bias current. We present numerical calculations to support our analytical results. We also discuss the existence and stability of excited states bifurcating from a uniform solution.