Spontaneous flux in a d-wave superconductor with   time-reversal-symmetry-broken pairing state at {110} boundaries
  The induction of an s-wave component in a d-wave superconductor is considered. Near the {110}-oriented edges of such a sample, the induced s-wave order parameter together with d-wave component forms a complex combination d+e^{i\phi} s, which breaks the time reversal symmetry (BTRS) of the pairing state. As a result, the spontaneous current is created. We numerically study the current distribution and the formation of the spontaneous flux induced by the current. We show that the spontaneous flux formed from a number of defect lines with {110} orientation has a measurable strength. This result may provide a unambiguous way to check the existence of BTRS pairing state at {110}-oriented boundaries. 
Jian-Xin Zhu and C. S. Ting