Helical Topological Edge States in a Quadrupole Phase

Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori

doi:10.1103/physrevlett.122.086804

Cited by 193 publications

(132 citation statements)

References 34 publications

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“…1 b. As a consequence, when the pseudospin–pseudospin coupling is considered in a finite-size structure, the pseudospins will have nonzero polarizations 39 . To observe these nonzero pseudospin polarizations, we experimentally fabricate a sample comprised of a second-order photonic topological insulator and a trivial topological insulator as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Higher-order quantum spin Hall effect in a photonic crystal

et al. 2020

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The quantum spin Hall effect lays the foundation for the topologically protected manipulation of waves, but is restricted to one-dimensional-lower boundaries of systems and hence limits the diversity and integration of topological photonic devices. Recently, the conventional bulkboundary correspondence of band topology has been extended to higher-order cases that enable explorations of topological states with codimensions larger than one such as hinge and corner states. Here, we demonstrate a higher-order quantum spin Hall effect in a twodimensional photonic crystal. Owing to the non-trivial higher-order topology and the pseudospin-pseudospin coupling, we observe a directional localization of photons at corners with opposite pseudospin polarizations through pseudospin-momentum-locked edge waves, resembling the quantum spin Hall effect in a higher-order manner. Our work inspires an unprecedented route to transport and trap spinful waves, supporting potential applications in topological photonic devices such as spinful topological lasers and chiral quantum emitters.

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Section: Introductionmentioning

confidence: 99%

Higher-order quantum spin Hall effect in a photonic crystal

et al. 2020

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“…The PC structure we proposed above is a simple implementation of the hexagonal Su-Schrieffer-Heeger (SSH) model [30,31] or the "shrink and expand" scheme proposed in Ref. [21].…”

Section: Pc Structure and The Emergence Of Nontrivial Pseudospin mentioning

confidence: 99%

Coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with C3v symmetry

Chen

Jiang

Lan

et al. 2020

Phys. Rev. Research

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We demonstrate the coexistence of pseudospin-and valley-Hall-like edge states in a photonic crystal with C 3v symmetry, which is composed of three interlacing triangular sublattices with the same lattice constants. By tuning the geometry of the sublattices, three complete photonic band gaps with nontrivial topology can be created, one of which is due to the band inversion associated with the pseudospin degree of freedom at the point and the other two due to the gapping out of Dirac cones associated with the valley degree of freedom at the K, K points. The system can support triband pseudospin-and valley-momentum locking edge states at properly designed domain-wall interfaces. Furthermore, to demonstrate the novel interplay of the two kinds of edge states in a single configuration, we design a four-channel system, where the unidirectional routing of electromagnetic waves against sharp bends between two routes can be selectively controlled by the pseudospin and valley degrees of freedom. Our work combines the pseudospin and valley degrees of freedom in a single configuration and may provide more flexibility in manipulating electromagnetic waves with promising potential for multiband and multifunctional applications.

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“…It has been shown, both theoretically and in recent experiments [9][10][11][12][13][14] , that a twodimensional (2D) quantised quadrupole TI exhibits topological states at "boundaries of boundaries": it lacks 1D topological edge states (unlike standard 2D TIs), but instead hosts topologically protected zero-dimensional (0D) corner states. This generalised bulk-boundary correspondence principle has opened the door to the pursuit of higher-order TIs [7][8][9][10][11][12][13][14][15][16][17][18][19] ; topological corner states in both 2D [9][10][11][12][13][14]20,21 and three-dimensional (3D) [22][23][24] systems have been observed, arising from not only quantised multipole moments [9][10][11][12][13][14] but also from quantised dipole moments [20][21][22][23][24] .…”

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confidence: 99%

Observation of an acoustic octupole topological insulator

et al. 2020

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Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on onedimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.

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Helical Topological Edge States in a Quadrupole Phase

Cited by 193 publications

References 34 publications

Higher-order quantum spin Hall effect in a photonic crystal

Higher-order quantum spin Hall effect in a photonic crystal

Coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with C3v symmetry

Observation of an acoustic octupole topological insulator

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