Oscillations of magnetization and conductivity in anisotropic Fulde-Ferrell-Larkin-Ovchinnikov superconductors

We derive the fluctuational magnetization and the paraconductivity of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors in their normal state. The FFLO superconducting fluctuations induce oscillations of the magnetization between diamagnetism and unusual paramagnetism which originates from the competition between paramagnetic and orbital effects. We also predict a strong anisotropy of the paraconductivity when the FFLO transition is approached in contrast with the case of a uniform BCS state. Finally building a Ginzburg-Levanyuk argument, we demonstrate that these fluctuation effects can be safely treated within the Gaussian approximation since the critical fluctuations are prominent only within an experimentally inaccessible temperature interval.

Figure 1

Minima of the fluctuation spectrum ${\epsilon }_{\mathbf{k}}$ for the two-dimensional model with square symmetry. The filled (open) ellipses indicate the locations of the lowest-energy fluctuations for $\eta >1$ $\left(\eta <1\right)$. Note that in the isotropic model $\left(\eta =1\right)$, there is an infinity of degenerate minima located on the circle (solid line).

Figure 2

Schematic field-temperature $\left(H,T\right)$ phase diagram showing the cascade of Landau levels. The thick dashed curve represents the critical field in the absence of orbital effect. In the presence of orbital effect, the critical field is reduced and described by the thin dashed curves which corresponds, respectively, to the $n=0$, $n=1$, and $n=2$ Landau levels. The solid line represents schematically the expected transition line between the normal and the superconducting states. The fluctuations are diamagnetic between zero field $\left(H=0,T_c\right)$ and $B$, paramagnetic near the arc AB, then again diamagnetic near the arc BC, etc. The Landau levels are degenerate at pointsB, D, etc. This schematic picture is relevant for both 2D FFLO superconductors and for 3D ones where the Landau-level modulation is realized [scenario (b) evoked in the introduction].