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arXiv:1104.0614

Unconventional Fulde-Ferrel-Larkin-Ovchinnikov states in spin-orbit coupled condensates: exact results

Qiang Han, Jia Liu, Dan-Bo Zhang, Z. D. Wang

Published Apr 4, 2011• 0 citations
arXivHTMLPDF

Abstract

We find that a model Hamiltonian of s-wave superconductors in the presence of spin-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensate.

DOI
10.48550/arxiv.1104.0614

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We find that a model Hamiltonian of s-wave superconductors in the presence of spin-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensate.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of a strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in ddd-wave superconductors. We investigate the FFLO state in a strongly correlated ddd-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and the Gutzwiller approximation. We find that the crucial effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp midgap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational-symmetry-breaking competing order in the ground state. This is demonstrated by considering a broken-symmetry ground state with a simultaneous presence of the ddd-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.
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.
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.
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 previously studied Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is stabilized by a magnetic field via the Zeeman coupling in spin-singlet superconductors. Here we suggest a novel route to achieve nonzero center-of-mass momentum pairing states in superconductors with Fermi surface nesting. We investigate two-dimensional superconductors under a uniform external current, proportional to a finite pair momentum of q(e). We find that an FFLO state with a spontaneous pair momentum of q(s) is stabilized above a certain critical current that depends on the direction of the external current. A finite q(s) arises in order to make the total pair-momentum of q(t)(=q(s) + q(e)) perpendicular to the nesting vector, which is independent of spin states of Cooper pairs. We also discuss experimental signatures of the FFLO state.