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Physical Review A

Entire set of dynamical excitations of a one-dimensional Fulde-Ferrell-pairing Fermi superfluid based on momentum excitation

Peng Zou, Huaisong Zhao, Feng Yuan, Shi-Guo Peng

Published May 20, 2024• 2 citations
Publisher

Abstract

We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field $h$ and study all of the 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 center-of-mass momentum $p$, there are two obvious gapless collective modes with different speeds and two kinds of continuous regimes related to single-particle excitation. The lower collective modes are from the usual gauge symmetry breaking and have a larger speed than the one in the negative direction of $p$. The higher one is due to the direction spontaneous symmetry breaking of center-of-mass momentum $p$ and separates a gapless lower-branch single-particle excitation from the other gapped higher-branch single-particle excitation in the positive $p$ direction. However, this higher mode disappears in the opposite direction of $p$, where two single-particle excitations overlap with each other. These signals of dynamical excitations could help to distinguish a Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in future experiments.

DOI
10.1103/physreva.109.053313

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We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field hhh and study all of the 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 center-of-mass momentum ppp, there are two obvious gapless collective modes with different speeds and two kinds of continuous regimes related to single-particle excitation. The lower collective modes are from the usual gauge symmetry breaking and have a larger speed than the one in the negative direction of ppp. The higher one is due to the direction spontaneous symmetry breaking of center-of-mass momentum ppp and separates a gapless lower-branch single-particle excitation from the other gapped higher-branch single-particle excitation 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 could help to distinguish a Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in future experiments.
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.
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 theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit-coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF, and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the xxx direction, the tensor component along the yyy direction ns,yy{n}_{s,yy}ns,yy​ is generally larger than ns,xx{n}_{s,xx}ns,xx​ in most parameter space. At zero temperature, there is always a discontinuity jump in ns,xx{n}_{s,xx}ns,xx​ as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit-coupling strength, interatomic interaction strength, and in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of 0.1TF0.1{T}_{F}0.1TF​, where TF{T}_{F}TF​ is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.
Determining the center-of-mass (COM) momentum of Cooper pairs in unconventional superconductors or superfluids is a topic of great interest in condensed matter physics and ultracold atomic gases. Theoretically, we investigate the dynamical excitations of a two-dimensional spin-polarized attractive Hubbard model on a square optical lattice under an effective Zeeman field by computing the density and spin dynamical structure factors, focusing on phase transition from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. In the FFLO superfluid, besides the phonon mode in the density channel, a low-energy bogolon mode emerges in the spin channel, which is associated with Bogoliubov quasiparticles on a Bogoliubov Fermi surface. Moreover, the dynamical excitations exhibit pronounced anisotropy in momentum space due to the finite COM momentum. At half filling, the roton mode around [ π , π ] evolves from a point-like minimum into a ring structure shifted by the COM momentum across the BCS-FFLO transition, providing a roton-based protocol to extract the COM momentum. These predictions provide key insights for confirming the existence of FFLO superfluids and understanding their dynamical excitation spectra.
Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.