Superconducting fluctuations near the FFLO state

The Fulde, Ferrell, Larkin and Ovchinnikov (FFLO) state consists in a modulation of the superconducting order parameter due to Zeeman effect. In a Ginzburg-Landau approach, higher order terms than usual in the gradient expansion, i.e. quartic terms, are needed to take into account the FFLO modulation. The role of this quartic term in addition to the quadratic usual term in a Gaussian fluctuation spectrum have been investigated for heat capacity C and paraconductivity s near a FFLO state for both isotropic and anisotropic cases. In the isotropic (resp. anisotropic) case, the power laws are drastically different (resp. similar) in comparison with the homogeneous superconductivity case. Nevertheless, for the anisotropic case the anisotropic ratio δxx/δyy is quite different for a FFLO phase than for a BCS one. In addition, we predict anomalous power laws near the tricritical point where the normal phase and the two superconducting (uniform and FFLO) phases are merging. The multiple crossovers associated with the phase transitions between homogeneous, tricritical and inhomogenous fluctuation regimes thus may serve as a powerful tool to identify the FFLO phases.