High-field superconducting phase diagrams including Fulde-Ferrell-Larkin-Ovchinnikov vortex states

Motivated by a striking observation of a Fulde-Ferell-Larkin-Ovchinnikov (FFLO) vortex state in the heavy fermion material CeCoIn(5) in fields perpendicular to the superconducting planes (H parallel to c), superconducting phase diagrams including an FFLO state of uniaxially anisotropic superconductors are systematically studied. In the ballistic limit with no quasiparticle (QP) relaxation, the high-field superconducting state in H parallel to c and in the low temperature limit should be not the FFLO state modulating along H, appearing in CeCoIn(5), but a different vortex state with a modulation perpendicular to the field. It is argued that an enhancement near H(c2)(0) of the QP relaxation rate, presumably originating from a nonsuperconducting quantum critical fluctuation, in this material is the origin of the absence of the latter modulated state and of the strange H parallel to c phase diagram in which the FFLO state is apparently different from that in H perpendicular to c.