d+is vs d+id' Time Reversal Symmetry Breaking States in Finite Size Systems

We report self-consistent quasiclassical calculations of spontaneous currents and magnetic moments in finite size unconventional superconducting systems, namely: (i) in isolated d-wave superconductor islands where, in addition to the dominant order parameter (with a d_{x^2-y^2} symmetry), a subdominant order parameter of s or d_{xy} symmetry is added; (ii) in grain boundary junctions between two arbitrarily oriented d-wave superconductors, and between a d-wave and an s-wave superconductor. We show that the profile of the spontaneous current density and the magnetic field distribution depend on the time-reversal symmetry breaking properties of the system. For the d_{x^2-y^2}+id_{xy} state, vortices appear near the edges of the finite size systems. We associate these vortices with the chiral nature of the mixed order parameter. The method developed here is quite general, and can be used for predicting properties of any finite size superconducting system.