We derive the generalized Ginzburg-Landau free energy functional for
conventional and unconventional singlet superconductors in the presence of
paramagnetic, orbital and impurity effects. Within the mean field theory, we
determine the criterion for appearence of the non uniform
(Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state, with vortex lattice
structure and additional modulation along the magnetic field. We also discuss
the possible change of the order of transition from normal to superconducting
state. We find that the superconducting phase diagram is very sensitive to
geometrical effects such as the nature of the order parameter and the shape of
the Fermi surface. In particular, we obtain the qualitative phase diagrams for
three-dimensional isotropic s-wave superconductors and in quasi two-dimensional
d-wave superconductors under magnetic field perpendicular to the conducting
layers.
In addition, we determine the criterion for instability toward non uniform
superconducting state in s-wave superconductors in the dirty limit.Comment: 15 pages, 4 figure