Semifluxons in 0–π–0 infinitely long Josephson junctions

•A 0–π–0 long Josephson junction on infinite domain is studied.•The stability of the uniform solutions in terms of facet length is discussed.•We show that in the instability region the ground states solutions are non-uniform.•The effect of bias current on the ground state is studied.•The critical current about the zero state is calculated analytically.

We investigate both analytically and numerically an infinitely long Josephson junction with two π-discontinuities in the phase characterized by a jump of π in the phase difference of the junction, i.e. a 0–π–0 long Josephson junction on an infinite domain. The dynamics of the system is described by a modified one-dimensional perturbed sine-Gordon equation. We investigate an instability region of the trivial zero solution in which semifluxons are spontaneously generated. A perturbation technique is used to show that the existence of static semifluxons depends on the length of the junction, the facet length, and the applied bias current. Numerical simulations are presented accompanying our analytical results.