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arXiv:2306.05868 · Physical Review A

Dynamic structure factor of two-dimensional Fermi superfluid with Rashba spin-orbit coupling

Huaisong Zhao, Xu Yan, Shi-Guo Peng, Peng Zou

Published Sep 8, 2023• 4 citations
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Abstract

We theoretically calculate the dynamic structure factor of a two-dimensional Rashba-type spin-orbit-coupled (SOC) Fermi superfluid with the random phase approximation and analyze the main characters of dynamical excitation shown by both density and spin dynamic structure factors during a continuous phase transition between a Bardeen-Cooper-Schrieffer superfluid and a topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to the two-branch structure of the quasiparticle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless $DD$-type pair-breaking excitation at the critical Zeeman field ${h}_{c}$ and is imparted a finite width to phonon peak when the transferred momentum $\mathit{q}$ is around the Fermi vector ${k}_{F}$. At a much larger transferred momentum $(\mathit{q}=4{k}_{F})$, the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without the SOC effect.

DOI
10.1103/physreva.108.033309

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We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation approach at zero temperature, and find their dynamical characters across the phase transition from a balanced conventional Bardeen-Cooper-Schrieffer (BCS) superfluid to a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a Bose-Einstein-condensate-like regime of the Fermi superfluid, dynamic structure factors can help distinguish the in-phase ground state from the out-of-phase metastable state by the relative location of molecular excitation and Leggett mode, or the minimum energy to break a Cooper pair. In the phase transition from BCS to Sarma superfluid, we find the dynamic structure factor of Sarma superfluid has its own specific gapless excitation at a small transferred momentum where the collective phonon excitation acquires a finite width, and also a relatively strong atomic excitation at a large transferred momentum, because of the existence of unpaired Fermi atoms. Our results can be used to differentiate Sarma superfluid from BCS superfluid.
We theoretically calculate the density dynamic structure factor of one-dimensional Fermi superfluid with Raman-type spin-orbit coupling, and analyze its main dynamical character during phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Our theoretical results display four kinds of single-particle excitations induced by the two-branch structure of the single-particle spectrum, and the cross single-particle excitation is much easier to see in the spin dynamic structure factor at a small transferred momentum. Also we find a new rotonlike collective mode emerges at a fixed transferred momentum $q\ensuremath{\simeq}2{k}_{F}$, and it only appears once the system enters the topological superfluid state. The occurrence of this rotonlike excitation is related to the switch of the global minimum in the single-particle spectrum from k=0k=0k=0 to $k\ensuremath{\simeq}2{k}_{F}$.
By calculating the dynamical structure factor of the two-dimensional doped attractive Fermi-Hubbard model with Rashba spin-orbit coupling (SOC), we not only investigate collective modes and single-particle excitations of the system during the phase transition between the Bardeen-Cooper-Schrieffer superfluid and topological superfluid, but also propose a universal method to measure the pairing gap in an optical lattice system. Our numerical results show that the area of the molecular excitation peak at the transferred momentum $\mathbf{q}=[\ensuremath{\pi},\ensuremath{\pi}]$ is proportional to the square of the pairing gap in the system with Rashba SOC. In particular, this method is very sensitive to the pairing gap. We verify that this method is universal to measure the pairing gap in a doped optical lattice with Rashba SOC. These theoretical results are important for experimentally measuring the pairing gap and studying the topological superfluid in an optical lattice.
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Abstract Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba spin–orbit coupling (SOC), the SOC strength and Zeeman field dependences of the phase diagram are investigated by calculating the pairing gap self-consistently. The results reveal that the phase transition from the BCS superfluid to the topological superfluid happens under proper Zeeman field strength and SOC strength. In particular, in contrast to the BCS superfluid decreasing monotonically as the SOC strength increasing, the topological superfluid region shows a dome with the SOC strength increasing. An optimal region in the phase diagram to find the topological superfluid can be found, which is important to realize the topological superfluid in optical lattice experimentally. Then we obtain the change of both band structure and density of states (DOSs) during the topological phase transition, and explain the four peaks of DOS in the topological superfluid by the topology change of the low-energy branch of quasiparticle energy spectra. Moreover, the topological superfluid can be suppressed by the doping concentration.
We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field hhh, and study entire dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of centre-of-mass momentum ppp, there are two obvious gapless collective modes with different speed. The lower collective modes is from the usual gauge symmetry breaking and has a larger speed than the one in the negative direction of ppp. The higher one is due to the direction spontaneous symmetry breaking of centre-of-mass momentum ppp, and separates two kinds of single-particle excitations in the positive ppp direction. However, this higher mode disappears in the opposite direction of ppp, where two single-particle excitations overlap with each other. These signals of dynamical excitations can do help to distinguish Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in the future experiment.