Effects of Pauli paramagnetism on superconducting vortex phase diagram in strong fields

The Ginzburg-Landau (GL) functional and the resultant phase diagram of quasi two-dimensional superconductors in strong fields perpendicular to the layers, where the Pauli paramagnetic depairing is not negligible, are examined in details by assuming the weak coupling BCS model with a dx2−y2 like pairing. It is found that the temperature at which the mean field (MF) transition at Hc2 changes into a discontinuous one lies much above another temperature at which a line HFFLO(T ) of transition to a helical FFLO-like vortex solid may begin to appear. In addition to MF results, details of a real phase diagram near Hc2(T )-line are examined based on a theoretical argument and Monte Carlo simulations, and it is found that the MF discontinuous transition is changed due to the fluctuation into a crossover which is nearly discontinuous in systems with weak enough fluctuation. These results are consistent both with the MF discontinuous behavior and a suggestion of HFFLO(T ) in the heavy fermion superconductor CeCoIn5 with weak fluctuation and with their absence in cuprate and organic superconductors with strong fluctuation.