AIII and BDI topological systems at strong disorder

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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“…for a loop L around the band crossing node [44][45][46]. Direct calculation yields C 1 = 1 in our case, and the corresponding Berry phase is π.…”

Section: And That the Berry Curvatures Read ωmentioning

confidence: 95%

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Xu¹,

Zhang²,

Zhang³

2015

Phys. Rev. Lett.

297

233

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“…Since in a given time frame α (= 1, 2), early studies [89] have established that w α = w α , we could finally state the bulk-edge correspondence of our PQSCL model as:…”

Section: Edge States and Bulk-edge Correspondencementioning

confidence: 99%

Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

Zhou

2020

Phys. Rev. A

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Floquet engineering has the advantage of generating new phases with large topological invariants and many edge states by simple driving protocols. In this work, we propose an approach to obtain Floquet edge states with fourfold degeneracy and even-integer topological characterizations in a spinful Creutz ladder model, which is realizable in current experiments. Putting the ladder under periodic quenches, we found rich Floquet topological phases in the system, which belong to the symmetry class CII. Each of these phases is characterized by a pair of even integer topological invariants (w0, wπ) ∈ 2Z × 2Z, which can take arbitrarily large values with the increase of driving parameters. Under the open boundary condition, we further obtain multiple quartets of topological edge states with quasienergies zero and π in the system. Their numbers are determined by the bulk topological invariants (w0, wπ) due to the bulk-edge correspondence. Finally, we propose a way to dynamically probe the Floquet topological phases in our system by measuring a generalized mean chiral displacement. Our findings thus enrich the family of Floquet topological matter, and put forward the detection of their topological properties. arXiv:1912.09078v1 [cond-mat.mes-hall]

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“…A generalization of the free fermion result to interacting cases has also been obtained for 1D systems [11][12][13][14][15][16]. Many efforts are devoted to construct models belonging to different classes in order to study different kinds of topological properties [17][18][19][20][21][22][23]. …”

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confidence: 99%

Kaleidoscope of symmetry-protected topological phases in one-dimensional periodically modulated lattices

Guo

Chen

2015

Phys. Rev. B

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We identify the existence of various symmetry-protected topological states in one-dimensional superlattices with periodically modulated hopping amplitudes or on-site potentials, which can be characterized by the quantized Berry phase π or the emergence of a pair of degenerate boundary states. It is shown that there may exist three types of topological phases, which are protected by the inversion symmetry, the chiral symmetry, and both of them, respectively, depending on the modulations, the odd or even modulation period. The connection between the hopping and potential modulations is also discussed. Furthermore, we demonstrate that the topological phase protected by the inversion symmetry can be realized in the interacting boson systems trapped in the same superlattices. The results are very possibly studied experimentally in the superlattice systems engineered with state-of-art technologies. Introduction.-The one-dimensional (1D) topological phases have attracted intense recent studies due to the experimental progress in hybrid superconductorsemiconductor wires [1,2], photonic crystals [3,4] and cold atomic gases [5]. The classification of 1D free fermion systems covering the time-reversal symmetry, particle-hole symmetry and chiral symmetry has been established and five out of ten symmetry classes are topological [6,7]. The inversion symmetry has also been included and the classification is considerably modified, such as: the AI class becomes topological; the topological invariant of the BDI class is replaced by a Z 2 number [8][9][10]. A generalization of the free fermion result to interacting cases has also been obtained for 1D systems [11][12][13][14][15][16]. Many efforts are devoted to construct models belonging to different classes in order to study different kinds of topological properties [17][18][19][20][21][22][23].

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AIII and BDI topological systems at strong disorder

Cited by 94 publications

References 36 publications

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids

Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

Kaleidoscope of symmetry-protected topological phases in one-dimensional periodically modulated lattices

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