Structure of the non-uniform Fulde-Ferrell-Larkin-Ovchinnikov state in 3D superconductors

We demonstrate that in 3D superconductors the transition between a normal phase and a non-uniform superconducting phase is always of the first order in the pure paramagnetic limit. We also determine the transition temperature and the structure of the modulated `lattice' by means of the generalized Ginzburg-Landau functional near the tricritical temperature, and the exact Gorkov equations in the whole temperature interval.