Temperature dependence of the upper critical field of an anisotropic singlet superconductivity in a square lattice tight-binding model in parallel magnetic fields

Upper critical field parallel to the conducting layer is studied in anisotropic type-II superconductors on square lattices. We assume enough separation of the adjacent layers, for which the orbital pair-breaking effect is suppressed for exactly aligned parallel magnetic field. In particular, we examine the temperature dependence of the critical field H_c(T) of the superconductivity including the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) state, in which the Cooper pairs have non-zero center-of-mass momentum q. In the system with the cylindrically symmetric Fermi-surface, it is known that H_c(T) of the d-wave FFLO state exhibits a kink at a low temperature due to a change of the direction of q in contrast to observations in organic superconductors. It is shown that the kink disappears when the Fermi-surface is anisotropic to some extent, since the direction of q is locked in an optimum direction independent of the temperature.