Vortex state in unconventional junctions of superconductors with d+is symmetry

Based on the Ginzburg-Landau theory, we derive a general current expression for a Josephson junction made of two superconductors with order parameters of different mixing of d-wave and s-wave symmetry. It is found that the characteristic phase φ_c occurring in the current-phase relation is crucially determined by the two-component order-parameter configuration. By solving the sine-Gordon equation constructed from this expression, we study the static properties of a frustrated Josephson junction consisting of two junctions with characteristic phases φ_c1 and φ_c2. In the short junction limit, the order-parameter symmetry can manifest in the diffraction pattern of the critical current passing through the junction. In the long junction limit, we show that a spontaneous vortex with the flux Φ₀[1-(φ_c2-φ_c1)/2π] is induced near the center of the junction. As a result, the interference pattern of the critical currents versus an applied magnetic field is insensitive to the order-parameter profile. These analyses could be used to describe both d+is-wave/s-wave superconducting corner junctions and d+is-wave tricrystal junctions.