Phase Diagram of the Fulde-Ferrell-Larkin-Ovchinnikov State in a Three-Dimensional Superconductor

The phase diagram of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a 3-dimensional superconductor is discussed. We use the quasi-classical Green's function to calculate the free energy. It is shown that the phase transition from the normal state is of first order at high temperatures but is of second order near T =0. To describe the phase transition in the Ginzburg-Landau theory, one has to take into account up to eighth order term with respect to the order parameter. The phase transition from the FFLO state to the uniform superconducting state is of second order in all the temperature range T <0.561 T c in accordance with Burkhardt and Rainer's result in a 2-dimensional system.