GENERALIZED GINZBURG-LANDAU THEORY FOR NONUNIFORM FFLO SUPERCONDUCTORS

We derive a generalized Ginzburg-Landau (GL) functional near the tricr itical point in the (T, H)-phase diagram for the Fulde-Ferrell-Larkin- Ovchinnikov (FFLO) superconducting state, in one, two, and three dimen sions. We find that the transition from the normal to the FFLO state i s of second order in one and two dimensions, and the order parameter w ith one-coordinate sine modulation corresponds to the lowest energy ne ar the transition line. We also compute the jump of the specific heat and describe in the one-dimensional case the transformation of the sin e modulation into the soliton-lattice state as the magnetic field decr eases. In three dimensions however, we find that the transition into a n FFLO state is of first order, and it is impossible to obtain an anal ytic expression for the critical temperature. In this case the general ized GL functional proposed here provides a suitable basis for a numer ical study of the properties of the FFLO state, and in particular for computing the critical temperature, and for describing the transition into a uniform state.