Topological Fulde–Ferrell superfluids of a spin–orbit coupled Fermi gas

Xu, Yong; Zhang, Chuanwei

doi:10.1142/s0217979215300017

Cited by 29 publications

(23 citation statements)

References 130 publications

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“…Realization in 3D FF superfluids-The toy model (2) may be applied to describe the band structures of solidstate materials or the quasiparticle spectra in superfluids or superconductors. Here we explore the latter possibility in realizing the structured Weyl points in a 3D SOC degenerate Fermi gas subject to Zeeman fields, where the dominant ground state phase is the FF superfluid [30][31][32][33][34].…”

Section: And That the Berry Curvatures Read ωmentioning

confidence: 99%

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Xu¹,

Zhang²,

Zhang³

2015

Phys. Rev. Lett.

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304

233

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We demonstrate that a Weyl point, widely examined in 3D Weyl semimetals and superfluids, can develop a pair of non-degenerate gapless spheres. Such a bouquet of two spheres is characterized by three distinct topological invariants of manifolds with full energy gaps, i.e., the Chern number of a 0D point inside one developed sphere, the winding number of a 1D loop around the original Weyl point, and the Chern number of a 2D surface enclosing the whole bouquet. We show that such structured Weyl points can be realized in the superfluid quasiparticle spectrum of a 3D degenerate Fermi gas subject to spin-orbit couplings and Zeeman fields, which supports Fulde-Ferrell superfluids as the ground state. [17,18]. A Weyl point can also be regarded as a monopole in 3D momentum space that exhibits an integer topological charge, i.e., the quantized first Chern number of a surface enclosing the singularity. Weyl points were also suggested to exist in the quasiparticle spectrum of superfluid 3 He A phase [2]. In contrast to traditional fully gapped superfluids, the Weyl superfluids bear doubly degenerate nodes pinned to zero energy, around which the quasiparticle energies disperse linearly in all directions. Most recently, the existence of such Weyl nodes has also been generalized to various coldatom superfluids and solid-state superconductors [19][20][21][22][23][24][25][26][27][28].In this Letter, we investigate whether a Weyl point can develop a nontrivial structure at zero energy and whether there exist any topological property protecting the developed structure. (i) We first consider a toy model to examine the possibility for a Weyl point to develop a gapless structure. Mathematically, the structured Weyl point can be viewed as a bouquet of two spheres (or wedge of two spheres) [29], which is a new class of topological state that has not been explored previously. Amazingly, the zero-energy bouquet is characterized by three distinct topological invariants: the first Chern number of a surface enclosing the whole bouquet, the zeroth Chern numbers of the interiors of the two spheres, and the winding number of a loop enclosing the touching point in the plane of symmetry. (ii) We further show that the structured Weyl points can be physically realized in the quasiparticle excitation spectrum of a 3D spin-orbit-coupled (SOC) fermionic cold-atom superfluid with the FuldeFerrell (FF) ground state. FF superfluids [30][31][32][33][34][35][36][37][38][39][40][41] have been studied recently in SOC degenerate Fermi gases subject to Zeeman fields, which yield asymmetries of the Fermi surface and induce the FF Cooper pairing with nonzero total momenta. We obtain a rich phase diagram in the gapless region of 3D FF superfluids, where not only the featureless Weyl points [19][20][21][22][23][24][25][26][27][28] but also the structured Weyl points emerge. Note that the featureless Weyl points have been well studied in SOC FF superfluids [24], and here we focus only on the novel structured Weyl points. (iii) We also discuss how the structured W...

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Section: And That the Berry Curvatures Read ωmentioning

confidence: 99%

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Xu¹,

Zhang²,

Zhang³

2015

Phys. Rev. Lett.

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304

233

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“…In a linear system, any superposition of the occupations in these minima is degenerate, which is the basis for many exotic phenomena when atomic interactions are taken into account [38,39]. In the case of a BEC, the degeneracy is broken by the mean-field energy, and the competition between the mean-field energy and SOC gives rise to new phases and phase transitions.…”

Section: Introductionmentioning

confidence: 99%

“…For degenerate Fermi gases, the role of SOC in the BEC-BCS crossover region has attracted a lot of attention [93][94][95]. In the BCS phase, unconventional states are predicted, such as Fulde-Ferrell-LarkinOvchinnikov (FFLO) superfluids [38]. Even though the field only started very recently, it has developed in a rapid fashion and several review articles on specific topics along this direction already exist [38,39,64,[96][97][98][99][100][101][102].…”

Section: Introductionmentioning

confidence: 99%

Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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The experimental and theoretical research of spin-orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin-orbit coupling parameters, we discuss the fundamental properties and general applications of spin-orbit-coupled Bose-Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin-orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin-orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin-orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

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“…This achievement has ignited tremendous interest in this field because of the dramatic change in the single particle dispersion (induced by spin-orbit coupling) which in conjunction with the interaction leads to many exotic superfluids [35][36][37][38][39][40][41][42][43][44][45](also see [46][47][48][49][50][51][52][53] for review). Such change in dispersion also results in exotic solitons even when the interaction is contact (without dipole-dipole interactions), including 1D bright solitons [54][55][56][57][58][59][60] for a BEC with attractive contact interactions, 1D dark [61,62] and gap solitons [63][64][65] for a BEC with repulsive contact interactions, as well as 1D dark solitons for Fermi superfluids [66,67].…”

Section: Introductionmentioning

confidence: 99%

Bright solitons in a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate

Zhang

2015

Phys. Rev. A

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We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate with repulsive contact interactions by both the variational method and the imaginary time evolution of the GrossPitaevskii equation. The dipoles are completely polarized along one direction in the 2D plane to provide an effective attractive dipole-dipole interaction. We find two types of solitons as the ground states arising from such attractive dipole-dipole interactions: a plane wave soliton with a spatially varying phase and a stripe soliton with a spatially oscillating density for each component. Both types of solitons possess smaller size and higher anisotropy than the soliton without spin-orbit coupling. Finally, we discuss the properties of moving solitons, which are nontrivial because of the violation of Galilean invariance.

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Topological Fulde–Ferrell superfluids of a spin–orbit coupled Fermi gas

Cited by 29 publications

References 130 publications

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Properties of spin–orbit-coupled Bose–Einstein condensates

Bright solitons in a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate

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