Switching Spinless and Spinful Topological Phases with Projective 
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 Symmetry

Zhao, Y. X.; Chen, Cong; Sheng, Xian‐Lei; Yang, Shengyuan A.

doi:10.1103/physrevlett.126.196402

Cited by 44 publications

(19 citation statements)

References 46 publications

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“…There are two important points that have not been appreciated in the study of topological states of matter. First, under a gauge field, crystal symmetries will be projectively represented, and this impacts the algebra of symmetry operations [11][12][13]. This can be understood from the analogy with Aharonov-Bohm effect [14]: the phase of wave function for different path is modified by the gauge field, which in turn revises the representation of spatial symmetries.…”

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confidence: 99%

“…Firstly, while our demonstration is in acoustics, the idea can also be realized in other classical systems like photonic/phononic crystals [15][16][17] and electric circuits [35]. Secondly, it would be interesting to explore more possibilities by increasing system dimension and considering other types of projective symmetries [11,13]. Besides, our system also provides a natural platform to study the effect of non-Hermiticity through introducing dissipation [36].…”

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confidence: 99%

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Projectively enriched symmetry and topology in acoustic crystals

Xue,

Wang,

Huang

et al. 2021

Preprint

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confidence: 99%

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confidence: 99%

Projectively enriched symmetry and topology in acoustic crystals

Xue,

Wang,

Huang

et al. 2021

Preprint

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“…The topological properties of quantum spectra in condensed matter systems got considerable attention in the past decade and are still under active consideration [1][2][3][4]. A large research field that has been formed thereby addresses gapped phases of insulators [5] and superconductors [6] characterized by globally defined topological numbers, and the edge modes [7] at the interfaces separating such phases.…”

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confidence: 99%

Abundance of Weyl points in semiclassical multi-terminal superconducting nanostructures

Barakov¹,

Nazarov²

2021

Preprint

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We show that the quasi-continuous gapless spectrum of Andreev bound states in multi-terminal semi-classical superconducting nanostructures exhibits a big number of topological singularities. We concentrate on Weyl points in a 4-terminal nanostructure, compute their density and correlations in 3D parameter space for a universal RMT model as well as for the concrete nanostructures described by the quantum circuit theory. We mention the opportunities for experimental observation of the effect in a quasi-continuous spectrum.

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“…The Z 2 gauge fields, namely allowing the (real) hopping amplitudes to take positive or negative signs, can be readily engineered in various artificial crystals, such as acoustic/photonic crystals [11][12][13][14], cold atoms in optical lattices [15][16][17], electric-circuit arrays [18,19], and mechanical systems [20,21]. The importance of projective symmetry algebras under Z 2 gauge fields has recently been emphasized [22][23][24], with fascinating consequences demonstrated in experiment [25,26]. Meanwhile, artificial crystals also enable simulations of higher-dimensional * zhaoyx@nju.edu.cn states by synthesized dimensions, e.g., 4D quantum Hall states has been demonstrated experimentally [27][28][29].…”

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confidence: 99%

Periodic Clifford symmetry algebras on flux lattices

Huang

Feng

et al. 2022

Phys. Rev. B

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Real Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the d-dimensional spinless rectangular lattices with π flux per plaquette. Due to the T -invariant flux configuration, real Clifford algebras are realized as projective symmetry algebras of lattice symmetries. Remarkably, d mod 8 exactly corresponds to the eight Morita equivalence classes of real Clifford algebras with eightfold Bott periodicity, resembling the eight real Altland-Zirnbauer classes. The representation theory of Clifford algebras determines the degree of degeneracy of band structures, both at generic k points and at high-symmetry points of the Brillouin zone. Particularly, we demonstrate that the large degeneracy at high-symmetry points offers a rich resource for forming novel topological states by various dimerization patterns, including a 3D higherorder semimetal state with double-charged bulk nodal loops and hinge modes, a 4D nodal surface semimetal with 3D surface solid-ball zero modes, and 4D Möbius topological insulators with a eightfold surface nodal point or a fourfold surface nodal ring. Our theory can be experimentally realized in artificial crystals by their engineerable Z2 gauge fields and capability to simulate higher dimensional systems.

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Switching Spinless and Spinful Topological Phases with Projective PT Symmetry

Cited by 44 publications

References 46 publications

Projectively enriched symmetry and topology in acoustic crystals

Projectively enriched symmetry and topology in acoustic crystals

Abundance of Weyl points in semiclassical multi-terminal superconducting nanostructures

Periodic Clifford symmetry algebras on flux lattices

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