Imbalancedd-wave superfluids in the BCS-BEC crossover regime at finite temperatures

Abstract

Singlet pairing in a Fermi superfluid is frustrated when the amounts of fermions of each pairing partner are unequal. The resulting 'imbalanced superfluid' has been realized experimentally for ultracold atomic gases with s-wave interactions. Inspired by high-temperature superconductivity, we investigate the case of d-wave interactions, and find marked differences from the s-wave superfluid. Whereas s-wave imbalanced Fermi gases tend to phase separate in real space, in a balanced condensate and an imbalanced normal halo, we show that the d-wave gas can phase separate in reciprocal space so that imbalance and superfluidity can coexist spatially. We show that the mechanism explaining this property is the creation of polarized excitations in the nodes of the gap. The Sarma mechanism, present only at nonzero temperatures for the s-wave case, is still applicable in the temperature zero limit for the d-wave case. As a result, the d-wave BCS superfluid is more robust with respect to imbalance, and a region of the phase diagram can be identified where the s-wave BCS superfluidity is suppressed whereas the d-wave superfluidity is not. When these results are extended into the BEC limit of strongly bound molecules, the symmetry of the order parameter matters less. The effects of fluctuations beyond mean field is taken into account in the calculation of the structure factor and the critical temperature. The poles of the structure factor (corresponding to bound molecular states) are less damped in the d-wave case as compared to s-wave. On the BCS side of the unitarity limit, the critical temperature T c follows the temperature T * corresponding to the pair binding energy and as such will also be more robust against imbalance. Possible routes for the experimental observation of the d-wave superfluidity have been discussed.

The Berezinskii–Kosterlitz–Thouless transition in imbalanced 2D Fermi gases: The role of fluctuations

“…[28]) of the NSR-like scheme. The results of this approach asymptotically tends to those obtained within the complete NSR-like approach [26,27] both in the weak-coupling and strong-coupling limits. The details of the derivation will be given in a more extended publication.…”

“…This NSR-like scheme has been extended to the case of unequal spin populations in Refs. [26,27]. We express the results below in terms of the averaged chemical potential l ¼ ðl " þ l # Þ=2 determining the total number of fermions and the chemical potential imbalance f ¼ ðl " À l # Þ=2.…”

Pseudogap and preformed pairs in the imbalanced Fermi gas in two dimensions

“…cannot be calculated analytically exactly. As in the analogous problem in 3D [2,38,39], and as explained in the introduction, we consider approximations provided by an expansion of the effective action S eff over fluctuations of the pair field x,τ about its saddle-point value . The phase diagrams of a 2D Fermi gas in the saddle-point approximation have been investigated in [37,40].…”

Phase correlations and quasicondensate in a two-dimensional ultracold Fermi gas

“…It is especially interesting to compare the decay of the phase correlations described by formulae (23) and (24) with the algebraic decay for a quasicondensate with the power index η ¼ 1=ðn s λ 2 T Þ following from the BKT theory.…”