Unconventional pairings of spin-orbit coupled attractive degenerate Fermi gas in a one-dimensional optical lattice

Abstract

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.

Phase diagram and topological superfluid state of spin-orbit coupled Fermi gas with attractive interactions in a one-dimensional optical lattice

“…A hallmark of the one-dimensional (1D) topological superfluids (TSF) is the emergence of boundary Majorana zero modes [10], which is believed to be a key ingredient for topological quantum computation [11] and attracted intensive recent studies [12][13][14][15][16][17][18][19][20][21]. The mechanism for realizing the TSF in spin-orbit coupled systems roots in the induced effective p-wave pairings [22], accompanied by the Zeeman field and pairing correlation, which comes from artificial mean-field treatment or proximity effect to the usual s-wave superconductors.…”

“…The Majorana-like quasizero modes are associated with interfaces between distinct phases that may form in different regions of the harmonic trap due to the spatial variation of the chemical potential. Another work regarding to the pairings of the spin-orbit coupled Fermi gas on a 1D optical lattice [13] has demonstrated the existence of exotic pairing states, including BCS pairing state, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and mixed pairing state where BCS and FFLO correlations coexist. However, some basic questions, i.e., whether an isolated 1D uniform quantum wire can support TSF states and how to characterize these states, are yet to be answered.…”

“…The strength of the on-site interaction U can be fine tuned by Feshbach resonance or confinement induced resonance [25], h is the strength of magnetic field, and the filling factor is defined as ν = N/L. The above model has the particle-hole symmetry which is invariant under the transformation [13] c i,σ → σ(−1) i d † i,−σ . Only filling ν ≤ 1 need to be considered.…”

“…Things will largely change if the SOC strength is set at the moderate strength. The system undergoes first from the BCS state to the mixed pairing state [13] then to the FFLO state or the metal state. The BCS, FFLO and mixed pairing phase can be distinguished by the s-wave pairing correlations in momentum space.…”

“…With the increase of the SOC strength, the k = 0 peak emerges. For α = 0.25, the exotic three-peak structure appears [13], corresponding to the so-called mixed pairing phase. Further increasing α, two peaks at finite momentums are suppressed.…”