Ginzburg-Landau theory of mixed wave superconductors

We address vortex state and dynamics of mixed wave superconductors in the framework of Ginzburg-Landau theory. We fmd that the s- and d-wave components of a single vortex in the d + is-state exhibit two-fold symmetry and the intrinsic Hall effect displays a different angle dependence from that of d-wave state. For d(x2-y2) + id(xy)-wave superconductors, a Ginzburg-Landau theory is developed from a microscopic theory with a strong coupling term being included. In the absence of a magnetic field, the theory predicts a pure d(x2-y2) state at T > T* and a second order phase transition at T* to a time-reversal-symmetry-breaking d(x2-y2) + id(xy) state, with T* being very small. In a magnetic field. the strong coupling effect could lead to that a d(x2-y2) + id(xy) state is always established, albeit with decreasing d(xy) amplitude with increasing temperature.