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arXiv:1305.2152 · Physical Review A

Competing superfluid orders in spin-orbit-coupled fermionic cold-atom optical lattices

Yong Xu, Chunlei Qu, Ming Gong, Chuanwei Zhang

Published Jan 10, 2014• 56 citations
arXivHTMLPDF

Abstract

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with nonzero total momentum Cooper pairs in a large magnetic field, was first predicted about 50 years ago and has since become an important concept in many branches of physics. Despite an intensive search in various materials, unambiguous experimental evidence for the FFLO phase is still lacking in experiments. In this paper we show that both Fulde-Ferrell (FF) (a uniform order parameter with a plane-wave phase) and Larkin-Ovchinnikov (LO) phases (a spatially varying order parameter amplitude) can be observed using fermionic cold atoms in spin-orbit-coupled optical lattices. The increasing spin-orbit coupling enhances the FF phase over the LO phase. The coexistence of superfluid and magnetic orders is also found in the normal BCS phase. The pairing mechanism for different phases is understood by visualizing superfluid pairing densities in different spin-orbit bands. The possibility of observing similar physics using spin-orbit-coupled superconducting ultrathin films is also discussed.

DOI
10.1103/physreva.89.013607

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The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with nonzero total momentum Cooper pairs in a large magnetic field, was first predicted about 50 years ago and has since become an important concept in many branches of physics. Despite an intensive search in various materials, unambiguous experimental evidence for the FFLO phase is still lacking in experiments. In this paper we show that both Fulde-Ferrell (FF) (a uniform order parameter with a plane-wave phase) and Larkin-Ovchinnikov (LO) phases (a spatially varying order parameter amplitude) can be observed using fermionic cold atoms in spin-orbit-coupled optical lattices. The increasing spin-orbit coupling enhances the FF phase over the LO phase. The coexistence of superfluid and magnetic orders is also found in the normal BCS phase. The pairing mechanism for different phases is understood by visualizing superfluid pairing densities in different spin-orbit bands. The possibility of observing similar physics using spin-orbit-coupled superconducting ultrathin films is also discussed.
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.
The recent experimental realization of spin-orbit (SO) coupling for ultracold atoms opens a completely new avenue for exploring new quantum matters. In experiments, the SO coupling is implemented simultaneously with a Zeeman field. Such SO-coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with nonzero center-of-mass momentum Cooper pairings, in contrast to the zero center-of-mass momentum pairings in Majorana superfluids. Therefore a natural question to ask is which phase, FFLO or Majorana superfluids, will survive in SO-coupled Fermi gases in the presence of a large out-of-plane Zeeman field. In this paper, we address this question by studying the mean-field quantum phases of 1D (quasi-1D) SO-coupled fermionic cold-atom optical lattices.
Fulde-Ferrell-Larkin-Ovchinnikov Superfluids with PPP-wave Symmetry in Spinless Fermionic Optical Lattices
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose Cooper pairing hosts a non-zero center-of-mass momentum, is predicted and well studied in spin-singlet superfluids in past decades. Different from previous works that engineer FFLO superfluids in spinful cold atoms, we show that the FFLO superfluids, with ppp-wave symmetry, can emerge in a spinless environment associated with nearest-neighbor-site interactions. The novel mechanism of the FFLO superfluids lies on the split Fermi surfaces at low filling factor, which naturally gives rise to Cooper pairings with finite momentum. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. The exotic topological transition can be explained by the spontaneously-broken translational invariance of order parameters. Finally, we investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature of the FFLO state, and show its possibility to be observed at finite temperature.
The realizations of spin-orbit coupling in cold atoms lead to a burst of research activities in the searching of topological matters in ultracold atom systems. Recent theoretical predictions show that topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids can be realized with appropriate spin-orbit coupling and in-plane Zeeman fields. In this work, a comprehensive understanding of the pairing symmetry, phase diagram, and the edge modes in this topological matter are presented. The center-of-mass momentum of the Cooper pairs plays the role of renormalizing the in-plane Zeeman fields and chemical potential. The in-plane Zeeman fields also induce asymmetry to the effective ppp-wave pairing, apart from a small fraction of higher orbital components. As a result, the phase diagram is composed by different phases, which are determined by the Fermi surface topology and band gap width of the superfluids. Especially, the gapped and gapless topological FFLO phases have totally different finite size effects. These features show that the spin-orbit coupled cold atoms provide an important platform in realizing topological matters which may not be materialized with solids.
The realizations of spin-orbit coupling in cold atoms lead to a burst of research activities in the searching of topological matters in ultracold atom systems. The very recent theoretical predictions show that topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids can be realized with proper spin-orbit coupling and Zeeman fields. In this work, a comprehensive understanding of the pairing symmetry, phase diagram and the edge modes in this new topological matter are presented. The momentum of the Cooper pairs plays the role of renormalizing the in-plane Zeeman field and chemical potential. The in-plane Zeeman field and finite momentum pairing induce asymmetry to the effective ppp-wave pairing, apart from a small fraction of higher orbital components. The phase diagram is composed by different phases, which are determined by the topology and band gap nature of the superfluids. Especially, the gapped and gapless topological FFLO phase have totally different finite size effect. These novel features show that the spin-orbit coupled cold atoms provides an important platform in realizing topological matters which may not be materialized with solids.
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids, Cooper pairings with finite momentum, and Majorana fermions (MFs), quasiparticles with non-Abelian exchange statistics, are two topics under intensive investigation in the past several decades, but unambiguous experimental evidence for them has not been found yet. Here we show that the recent experimentally realized shaken optical lattice provides a pathway to realize FFLO superfluids and MFs. By tuning the shaking frequency and amplitude, various couplings between the sss and ppp orbitals of the lattice (called the pseudospins) can be generated. We show that the combination of the sss- and ppp-band dispersion inversion, the engineered pseudospin coupling, and the on-site attractive interaction naturally allows the observation of FFLO superfluids as well as MFs in different parameter regions.