Gapless Topological Fulde-Ferrell Superfluidity in Spin-Orbit Coupled Fermi Gases

Cao, Ye; Zou, S. H.; Liu, Xia-Ji; Yi, Su; Long, Gui Lu; Hu, Hui

doi:10.1103/physrevlett.113.115302

Cited by 50 publications

(60 citation statements)

References 55 publications

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“…Recently, the spin-orbit coupling (SOC) has been realized by ultracold atoms as condensates or on an optical lattice [16][17][18][19], which paves the way to the topological FFLO states [20][21][22][23][24][25]. Theoretical researches show that topological FFLO states can be induced in one and two dimensional Fermi gas.…”

Section: Introductionmentioning

confidence: 99%

Topological Fulde-Ferrell superfluids in triangular lattices

Guo

2017

Phys. Rev. A

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Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) phases were proposed for superconductors or superfluids in strong magnetic field. With the experimental progresses in ultracold atomic systems, topological FFLO phases has also been put forward, since it is a natural consequence of realizable spin-orbital coupling (SOC). In this work, we theoretically investigate a triangular lattice model with SOC and in-plane field. By constructing the phase diagram, we show that it can produce topological FF states with Chern numbers, C = ±1 and C = −2. We get the phase boundaries by the change of the sign of Pfaffian. The chiral edge states for different topological FF phases are also elucidated.

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Section: Introductionmentioning

confidence: 99%

Topological Fulde-Ferrell superfluids in triangular lattices

Guo

2017

Phys. Rev. A

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“…(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.…”

mentioning

confidence: 99%

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Xu¹,

Zhang²,

Zhang³

2015

Phys. Rev. Lett.

298

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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“…The BKT transition temperature T BKT can be obtained from the superfluid weight tensor by using the generalized KT-Nelson criterion [56] for the anisotropic superfluid [12,49]:…”

Section: Derivation Of the Superfluid Weight In The Presence Of Soc Fmentioning

confidence: 99%

Superfluid weight and Berezinskii–Kosterlitz–Thouless temperature of spin-imbalanced and spin–orbit-coupled Fulde–Ferrell phases in lattice systems

2018

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We study the superfluid weight D s and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures T BKT in case of exotic Fulde-Ferrell (FF) superfluid states in lattice systems. We consider spinimbalanced systems with and without spin-orbit coupling (SOC) accompanied with in-plane Zeeman field. By applying mean-field theory, we derive general equations for D s and T BKT in the presence of SOC and the Zeeman fields for 2D Fermi-Hubbard lattice models, and apply our results to a 2D square lattice. We show that conventional spin-imbalanced FF states without SOC can be observed at finite temperatures and that FF phases are further stabilized against thermal fluctuations by introducing SOC. We also propose how topologically non-trivial SOC-induced FF phases could be identified experimentally by studying the total density profiles. Furthermore, the relative behavior of transverse and longitudinal superfluid weight components and the role of the geometric superfluid contribution are discussed.performed with quasi-one-dimensional population-imbalanced atomic gases have shown to be consistent with the existence of the FFLO state [33] but unambiguous proof is still missing.In addition to conventional spin-imbalanced quantum gas experiments, recently also synthetic SOC and Zeeman fields have been realized in ultracold gas experiments [34][35][36][37][38] which makes it possible to investigate SOC-induced FFLO states as well. As SOC-induced FFLO states have been predicted to be stable in larger parameter regime than conventional spin-imbalanced FFLO phases [10], synthetic SOC could provide a way to realize FFLO experimentally in ultracold gas systems [15].Low dimensionality has been predicted to favor 40]. However, in two and lower dimensional systems thermal phase fluctuations of the Cooper pair wave functions prevent the formation of true superfluid long range order as stated by the Mermin-Wagner theorem [41]. Instead, only quasi-long range order is possible. In two-dimensions, the phase transition from a normal Fermi gas to a superfluid state of quasi-long range order is determined by the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T BKT [42]. Below T BKT the system is a superfluid and above T BKT superfluidity is lost.In recent years, SOC-induced FFLO phases in two-dimensional systems have gained considerable attention [7,10,13,14,20,21,25]. In these systems it has been argued that SOC accompanied with the in-plane Zeeman field would yield FFLO states. Furthermore, in [13,14] it was predicted that in the presence of the out-of-plane Zeeman field, i.e. spin-imbalance, SOC-induced FFLO states could be topologically non-trivial and support Majorana fermions. Such topological FFLO states are conceptually new and exotic superconductive phases of matter. However, these studies were performed by applying mean-field theories which do not consider the stability of FFLO states against thermal phase fluctuations in terms of the BKT transition. Superfluidity and BKT transition temperatures of BCS phases in spin-...

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Gapless Topological Fulde-Ferrell Superfluidity in Spin-Orbit Coupled Fermi Gases

Cited by 50 publications

References 55 publications

Topological Fulde-Ferrell superfluids in triangular lattices

Topological Fulde-Ferrell superfluids in triangular lattices

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Superfluid weight and Berezinskii–Kosterlitz–Thouless temperature of spin-imbalanced and spin–orbit-coupled Fulde–Ferrell phases in lattice systems

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