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Communications in Theoretical Physics

Anisotropic dynamic excitations of a two-dimensional weakly interacting Fermi superfluid gas with Raman-type spin–orbit coupling

Shuning Tan, Jiayi Shi, Peng Zou, Tianxing Ma, Huaisong Zhao

Published May 26, 2026• 0 citations
Publisher

Abstract

Abstract Exploring anisotropic dynamics in exotic superconductors or superfluids with spin–orbit coupling (SOC) is essential for understanding the role of SOC in these systems. We theoretically calculate the density dynamical structure factor of a two-dimensional Fermi superfluid with Raman-type SOC and investigate its primary anisotropic dynamical characteristics under varying SOC strengths during the Lifshitz phase transition. Owing to the recoil momentum of the SOC laser beam, both the collective phonon mode and the single-particle excitations exhibit distinct anisotropic behavior. In contrast to superfluids without SOC, the phonon mode under SOC not only has a shorter lifetime due to stronger competition with single-particle excitations but also exhibits an anisotropic sound velocity. The sound velocity initially decreases and then increases as the SOC strength increases. Moreover, three types of threshold energies for single-particle excitations to break Cooper pairs are identified, which elucidate the complex edge curves of the dynamical structure factor.

DOI
10.1088/1572-9494/ae7272

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Abstract Exploring anisotropic dynamics in exotic superconductors or superfluids with spin–orbit coupling (SOC) is essential for understanding the role of SOC in these systems. We theoretically calculate the density dynamical structure factor of a two-dimensional Fermi superfluid with Raman-type SOC and investigate its primary anisotropic dynamical characteristics under varying SOC strengths during the Lifshitz phase transition. Owing to the recoil momentum of the SOC laser beam, both the collective phonon mode and the single-particle excitations exhibit distinct anisotropic behavior. In contrast to superfluids without SOC, the phonon mode under SOC not only has a shorter lifetime due to stronger competition with single-particle excitations but also exhibits an anisotropic sound velocity. The sound velocity initially decreases and then increases as the SOC strength increases. Moreover, three types of threshold energies for single-particle excitations to break Cooper pairs are identified, which elucidate the complex edge curves of the dynamical structure factor.
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 $k\ensuremath{\simeq}2{k}_{F}$.
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 DDDDDD-type pair-breaking excitation at the critical Zeeman field hc{h}_{c}hc​ and is imparted a finite width to phonon peak when the transferred momentum q\mathit{q}q is around the Fermi vector kF{k}_{F}kF​. At a much larger transferred momentum (q=4kF)(\mathit{q}=4{k}_{F})(q=4kF​), the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without the SOC effect.
We performed a theoretical investigation on the ground state properties of a two dimensional ultra-cold Fermi superfluid with an anisotropic spin-orbit coupling (SOC). In the absence of Zeeman field, the system evolves from weak coupling BCS regime to strongly interacting BEC regime (BCS-BEC crossover) with increasing either the two-particle interaction strength or SOC parameters. We focused on the behaviors of pairing parameter and density of states (DOS) when increasing the anisotropic parameter of the SOC. Surprisingly, we discovered that the gap parameter decreases with increasing the anisotropic parameters, but the DOS at the Fermi surface shows non-monotonic behavior as a function of the anisotropic parameter. In the presence of the Zeeman field, we discussed a particular type of topological phase transition by obtaining the analytical result of the topological invariant and directly related this quantum phase transition with a sudden change of the ground state wave-function. Effects of higher partial wave pairing terms on this topological phase transition were briefly discussed.
We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.
We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature T(BKT) is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.
We investigate the effects of Rashba-type spin-orbit coupling (SOC) on the condensed density and superfluid density tensor of a two-component Fermi gas in the BCS-BEC crossover at zero temperature. In anisotropic three dimensions (3D), we find that SOC has an opposite effect on condensation (enhanced) and superfluidity (suppressed in the SOC direction), and this effect becomes most pronounced for very weak interactions and the SOC strength being larger than a characteristic value. Furthermore, as functions of SOC strength, the condensed density changes monotonically for all interaction parameters, while the superfluid density has a minimum when the interaction parameter is below a critical value. We also discuss the isotropic two-dimensional case where analytical expressions for the gap and number equations are obtained and the same phenomena are found as that of the 3D case.