  Motivated by a striking observation of a Fulde-Ferell-Larkin-Ovchinnikov
(FFLO) vortex state in the heavy fermion material CeCoIn5 in fields {\it
perpendicular} to the superconducting planes (${\bf H} \parallel c$),
superconducting phase diagrams including an FFLO state of quasi two-dimensional
(Q2D) superconductors are systematically studied. In the clean {\it limit}, the
high field superconducting state in the low temperature limit should be not the
FFLO state modulating along ${\bf H}$, appeared in CeCoIn5 in both ${\bf H}
\parallel c$ and ${\bf H} \perp c$, but a different vortex state with a
modulation, induced by the paramagnetism, perpendicular to the field. It is
found that the presence of weak impurities is the origin of the absence in
CeCoIn5 of the latter state and leads to the ${\bf H} \parallel c$ phase
diagram, as seen in CeCoIn5, {\it apparently} different in character from that
in ${\bf H} \perp c$.

Superconductivity