Quantized non-Abelian, Berry's flux and higher-order topology of Na$_3$Bi

C., Tyner, Alexander; Sur, Shouvik; Zhou, Qunfei; Puggioni, Danilo; Darancet, Pierre; Rondinelli, James M.; Goswami, Pallab

doi:10.48550/arxiv.2102.06207

Cited by 5 publications

(7 citation statements)

References 47 publications

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“…We note that a non-trivial bulk invariant [35] has also been computed for Na 3 Bi in Ref. [66], but the corner states were not computed.…”

Section: Application To Na3bimentioning

confidence: 99%

Classification of Dirac points with higher-order Fermi arcs

Fang,

Cano

2021

Preprint

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Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with four-fold rotation symmetry have been shown to exhibit a higher order bulk-hinge correspondence: they display "higher order Fermi arcs," which are localized on hinges where two surfaces meet and connect the projections of the bulk Dirac points. In this paper, we classify higher order Fermi arcs for Dirac semimetals protected by a rotation symmetry and the product of time-reversal and inversion. Such Dirac points can be either linear in all directions or linear along the rotation axis and quadratic in other directions. By computing the filling anomaly for momentum-space planes on either side of the Dirac point, we find that all linear Dirac points exhibit higher order Fermi arcs terminating at the projection of the Dirac point, while the Dirac points that are quadratic in two directions lack such higher order Fermi arcs. When higher order Fermi arcs do exist, they obey either a Z2 (four-fold rotation axis) or Z3 (three-or six-fold rotation axis) group structure. Finally, we build two models with six-fold symmetry to illustrate the cases with and without higher order Fermi arcs. We predict higher order Fermi arcs in Na3Bi.

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“…We note that a non-trivial bulk invariant [35] has also been computed for Na 3 Bi in Ref. [66], but the corner states were not computed.…”

Section: Application To Na3bimentioning

confidence: 99%

Classification of Dirac points with higher-order Fermi arcs

Fang,

Cano

2021

Preprint

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“…These topological DSMs demonstrate 1D hinge Fermi arc states that terminate on the projection of Dirac nodes, which are dubbed higher-order DSMs. [10][11][12][13][14][15] Floquet engineering [16][17][18] has emerged as a powerful tool for realizing novel topological phases in quantum materials. It involves using time-periodic perturbations, such as light, to tailor band structures and topology of the quantum materials.…”

Section: Introductionmentioning

confidence: 99%

“…The first experimental verified topological DSM Na 3 Bi [83] belongs to C 6 symmetric topological DSM. Recently, Na 3 Bi is also predicted to host higher-order hinge Fermi arc states, [12,13,15] thus serving as a C 6 symmetric higher-order DSM candidate. The study of the Floquet topological phases in C 6 symmetric higher-order DSMs is desirable as it will provide an opportunity for the realization of controllable higher-order WSM [84][85][86] in solid materials.…”

Section: Introductionmentioning

confidence: 99%

Photoinduced Floquet higher-order Weyl semimetal in C₆ symmetric Dirac semimetals

Xu 许,

Wang 王,

Xu 许

et al. 2024

Chinese Phys. B

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Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges. Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

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“…Computation of the Chern-Simons invariant is generally considered to be impractical in many-band tight-binding (TB) models and Ab initio data, despite its relevance in a wide range of systems such as the recently proposed class of chiral higher-order topological insulators (HOTIs) 32 . In order to substantiate the connection between κ AF and third-homotopy we perform a joint analysis of planar Wilson loops (PWL) 33,34 and Wilson lines (WLs) [23][24][25][26][27][28][29] . For a single band to support a three dimensional winding number, we must be able to identify linked, closed curves supporting a π Berry's phase 4,6,35,36 ; PWLs and WLs identify closed curves of π non-Abelian Berry's phase in-plane and along cycles of the Brillouin zone (BZ) respectively, accommodating linking.…”

Section: Introductionmentioning

confidence: 99%

Part I: Staggered index and 3D winding number of Kramers-degenerate bands

C.¹,

Goswami²

2021

Preprint

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The symmetry-indicators provide valuable information about the topological properties of band structures in real materials. For inversion-symmetric, non-magnetic materials, the pattern of parity eigenvalues of various Kramers-degenerate bands at the time-reversal-invariant momentum points are generally analyzed with the combination of strong Z4, and weak Z2 indices. Can the symmetry indicators identify the tunneling configurations of SU(2) Berry's connections or the threedimensional, winding numbers of topologically non-trivial bands? In this work, we perform detailed analytical and numerical calculations on various effective tight-binding models to answer this question. If the parity eigenvalues are regarded as fictitious Ising spins, located at the vertices of Miller hypercube, the strong Z4 index describes the net ferro-magnetic moment, which is shown to be inadequate for identifying non-trivial bands, supporting even integer winding numbers. We demonstrate that an "anti-ferromagnetic" index, measuring the staggered magnetization can distinguish between bands possessing zero, odd, and even integer winding numbers. The coarse-grained analysis of symmetry-indicators is substantiated by computing the change in rotational-symmetry-protected, quantized Berry's flux and Wilson loops along various high-symmetry axes. By simultaneously computing ferromagnetic and anti-ferromagnetic indices, we categorize various bands of bismuth, antimony, rhombohedral phosphorus, and Bi2Se3.

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Quantized non-Abelian, Berry's flux and higher-order topology of Na$_3$Bi

Cited by 5 publications

References 47 publications

Classification of Dirac points with higher-order Fermi arcs

Classification of Dirac points with higher-order Fermi arcs

Photoinduced Floquet higher-order Weyl semimetal in C₆ symmetric Dirac semimetals

Part I: Staggered index and 3D winding number of Kramers-degenerate bands

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Quantized non-Abelian, Berry's flux and higher-order topology of Na$_3$Bi

Cited by 5 publications

References 47 publications

Classification of Dirac points with higher-order Fermi arcs

Classification of Dirac points with higher-order Fermi arcs

Photoinduced Floquet higher-order Weyl semimetal in C6 symmetric Dirac semimetals

Part I: Staggered index and 3D winding number of Kramers-degenerate bands

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Photoinduced Floquet higher-order Weyl semimetal in C₆ symmetric Dirac semimetals