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

Abstract

Motivated by a striking observation of a Fulde-Ferell-Larkin-Ovchinnikov (FFLO) vortex state in the heavy fermion material $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_{5}$ in fields perpendicular to the superconducting planes $(\mathbf{H}\ensuremath{\Vert}c)$, 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 $\mathbf{H}\ensuremath{\Vert}c$ and in the low temperature limit should be not the FFLO state modulating along $\mathbf{H}$, appearing in $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_{5}$, 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 $\mathbf{H}\ensuremath{\Vert}c$ phase diagram in which the FFLO state is apparently different from that in $\mathbf{H}\ensuremath{\perp}c$.