Generalized Ginzburg-Landau theory for nonuniform FFLO superconductors

We derive a generalized Ginzburg-Landau (GL) functional near the tricritical point in the (T, H)-phase diagram for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, in one, two, and three dimensions. We find that the transition from the normal to the FFLO state is of second order in one and two dimensions, and the order parameter with one-coordinate sine modulation corresponds to the lowest energy near the transition line. We also compute the jump of the specific heat and describe in the one-dimensional case the transformation of the sine modulation into the soliton-lattice state as the magnetic field decreases. In three dimensions however, we find that the transition into an FFLO state is of first order, and it is impossible to obtain an analytic expression for the critical temperature. In this case the generalized GL functional proposed here provides a suitable basis for a numerical 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.