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arXiv:1304.1473 · Physical Review A

Spin-orbit-coupling-induced Fulde-Ferrell-Larkin-Ovchinnikov-like Cooper pairing and skyrmion-like polarization textures in optical lattices

M. Iskin

Published Jul 25, 2013• 31 citations
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Abstract

We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.

DOI
10.1103/physreva.88.013631

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We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.
We use the Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.
Understanding novel pairings in attractive degenerate Fermi gases is crucial for exploring rich superfluid physics. In this report, we reveal unconventional pairings induced by spin-orbit coupling (SOC) in a one-dimensional optical lattice, using a state-of-the-art density-matrix renormalization group method. When both bands are partially occupied, we find a strong competition between the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings. In particular, for the weak and moderate SOC strengths, these two pairings can coexist, giving rise to a new phase called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. For the strong SOC strength, the intraband BCS pairing always dominates in the whole parameter regime, including the half filling. We figure out the whole phase diagrams as functions of filling factor, SOC strength, and Zeeman field. Our results are qualitatively different from recent mean-field predictions. Finally, we address that our predictions could be observed in a weaker trapped potential.
Recently a scheme has been proposed for generating the two-dimensional Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al., Phys. Rev. A 93, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the Bogoliubov---de Gennes simulations with a weak harmonic trap added.
We consider the quasi-one-dimensional (quasi-1D) system realized by an array of weakly coupled parallel one-dimensional ``tubes'' in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin-orbit coupling (SOC), and an sss-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T=0T=0T=0) Bogoliubov--de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes and show that the T=0T=0T=0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with nonzero center-of-mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center-of-mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the three-dimensional and 1D systems and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one dimensional. We also find evidence of the existence of a Zeeman-tuned topological quantum phase transition (TQPT) within the FFLO phase itself and, for large values of the Zeeman field and small SOC, the TQPT gives rise to a topologically distinct FFLO phase.
Pairings are the heart for exploring novel superfluid physics of degenerate fermi gases. In the presence of spin-orbit coupling (SOC), some exotic pairings, including the triplet ppp-wave pairing, have been predicted, which paves a new way to search topological superfluids and associated Majorana fermions. In this work, we reveal unconventional pairings induced by SOC in a one-dimensional optical lattice, using the exact density-matrix renormalization group. In the weak SOC, we find the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings may coexist, when both bands are partially occupied. This interesting coexistence can lead to a new quantum state, called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. However, in the intermediate and strong SOCs, the intraband BCS pairing dominates in the whole parameter regime. These results shed great light on the realization of topological superfluids in the spin-orbit coupled lattice.
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases under a Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well known that the system is either a Bardeen-Cooper-Schrieffer superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zero-energy Majorana modes. However, in the weakly interacting regime the topological superfluid prefers to stay at the trap edge, in contrast to a FFLO superfluid, which occurs near the trap center. As a result, it is unlikely to experimentally observe an inhomogeneous FFLO superfluid with topo-logical order without specifically tailoring the geometry or other parameters of the Fermi cloud.