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arXiv:1703.00161 · Physical review. B./Physical review. B

Instability of Fulde-Ferrell-Larkin-Ovchinnikov states in atomic Fermi gases in three and two dimensions

Jibiao Wang, Yanming Che, Leifeng Zhang, Qijin Chen

Published Apr 16, 2018• 26 citations
arXivHTMLPDF

Abstract

The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states have been actively searched for experimentally since the mean-field based FFLO theories were put forward half a century ago. Here, we investigate the stability of FFLO states in the presence of pairing fluctuations. We conclude that FFLO superfluids cannot exist in continuum in three and two dimensions, due to their intrinsic instability, associated with infinite quantum degeneracy of the pairs. These results address the absence of convincing experimental observations of FFLO phases in both condensed matter and in ultracold atomic Fermi gases with a population imbalance. We predict that the true ground state has a pair momentum distribution highly peaked on an entire constant energy surface.

DOI
10.1103/physrevb.97.134513

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The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states have been actively searched for experimentally since the mean-field based FFLO theories were put forward half a century ago. Here, we investigate the stability of FFLO states in the presence of pairing fluctuations. We conclude that FFLO superfluids cannot exist in continuum in three and two dimensions, due to their intrinsic instability, associated with infinite quantum degeneracy of the pairs. These results address the absence of convincing experimental observations of FFLO phases in both condensed matter and in ultracold atomic Fermi gases with a population imbalance. We predict that the true ground state has a pair momentum distribution highly peaked on an entire constant energy surface.
We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. By including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.
The ground-state phase diagram of attractively interacting Fermi gases in two dimensions with a population imbalance is investigated. We find the regime of stability for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, in which pairing occurs at a finite wave vector, and determine the magnitude of the pairing amplitude $\mathrm{\ensuremath{\Delta}}$ and FFLO wave vector qqq in the ordered phase, finding that $\mathrm{\ensuremath{\Delta}}$ can be of the order of the two-body binding energy. Our results rely on a careful analysis of the zero-temperature gap equation for the FFLO state, which possesses nonanalyticities as a function of $\mathrm{\ensuremath{\Delta}}$ and qqq, invalidating a Ginzburg-Landau expansion in small $\mathrm{\ensuremath{\Delta}}$.
In ultracold Fermi gases, the effect of spin imbalance on superfluidity has been the subject of intense study. One of the reasons for this is that spin imbalance frustrates the Bardeen-Cooper-Schrieffer (BCS) superfluid pairing mechanism, in which fermions in different spin states combine into Cooper pairs with zero momentum. In 1964, it was proposed that an exotic superfluid state called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the Cooper pairs have nonzero momentum, could exist in a spin-imbalanced Fermi gas. At the saddle-point (mean-field) level, it has been shown that the FFLO state only occupies a very small sliver in the ground-state phase diagram of a three-dimensional (3D) Fermi gas. However, a question that remains to be investigated is as follows: What is the influence of phase fluctuations on the FFLO state? In this work, we show that phase fluctuations only lead to relatively small quantitative corrections to the presence of the FFLO state in the saddle-point phase diagram of a 3D spin-imbalanced Fermi gas. Starting from the partition function of the system, we calculate the effective action within the path-integral adiabatic approximation. The action is then expanded up to second order in the fluctuation field around the saddle point, leading to the fluctuation free energy. Using this free energy, we calculate corrections due to phase fluctuations to the BCS-FFLO transition in the saddle-point phase diagram. At temperatures at which the FFLO state exists, we find only small corrections to the size of the FFLO area. Our results suggest that fluctuations of the phase of the FFLO order parameter, which can be interpreted as an oscillation of its momentum vector, do not cause an instability of the FFLO state with respect to the BCS state.
The recent development of experimental techniques in ultracold atomic Fermi gases is extremely helpful in the progress of the realization of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase in quasi-one dimensional systems (Liao et al 2010 Nature 467 567). Due to a Fermi surface nesting, which is enhanced in 1D, the low-dimensional systems are particularly good candidates to find the FFLO phase stable. We investigate the influence of a dimensional crossover (from one dimension (1D) to two dimensions (2D) or three dimensions (3D)) on the stability of the FFLO state in the spin-imbalanced attractive Hubbard model.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was first predicted in two-dimensional superconductors about 50 years ago, but so far unambiguous experimental evidence is still lacking. The recently experimentally realized spin-imbalanced Fermi gases may potentially unveil this elusive state, but they require very stringent experimental conditions. In this Rapid Communication, we show that FFLO phases may be observed even in a three-dimensional (3D) degenerate Fermi gas with spin-orbit coupling and an in-plane Zeeman field. The FFLO phase is driven by the interplay between the asymmetry of the Fermi surface and the superfluid order, instead of the interplay between magnetic and superconducting order in solid materials. The predicted FFLO phase exists in a giant parameter region, possesses a stable long-range superfluid order due to the 3D geometry, and can be observed with an experimentally already achieved temperature ($T\ensuremath{\sim}0.05{E}_{F}$), thus opening a fascinating avenue for exploring FFLO physics.
We investigate properties of exotic pairing states in a three-dimensional Fermi gas with three-dimensional spin-orbit coupling and an effective Zeeman field. The interplay of spin-orbit coupling, effective Zeeman field, and pairing can lead to first-order phase transitions between different phases, and to interesting nodal superfluid states with gapless surfaces in the momentum space. We then demonstrate that pairing states with zero center-of-mass momentum are unstable against Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, with a finite center-of-mass momentum opposite to the direction of the effective Zeeman field. Unlike conventional FFLO states, these FFLO states are induced by the coexistence of spin-orbit coupling and Fermi surface deformation, and have intriguing features like first-order transitions between different FFLO states, nodal FFLO states with gapless surfaces in momentum space, and exotic fully gapped FFLO states. With the recent theoretical proposals for realizing three-dimensional spin-orbit coupling in ultracold atomic gases, our work is helpful for future experimental studies and provides valuable information for the general understanding of pairing physics in spin-orbit-coupled fermionic systems.