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-root weak, Chern, and higher-order topological insulators, and 
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-root topological semimetals

Marques, A. M.; Dias, R. G.

doi:10.1103/physrevb.104.165410

Cited by 31 publications

(16 citation statements)

References 82 publications

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“…Moreover, it is worth noting that the concept of square-root topology has been extended to 2 n -root topological insulators, topological semimetals, and other HOTI creatures. 53,54 In this work we experimentally demonstrate the first photonic square-root HOTI. The photonic platform relies on judiciously designed lattice structures, the so-called decorated honeycomb lattices (HCLs) illustrated in Figure 1a, which simultaneously possess a Lieb-like pseudospin-1 and several graphene-like pseudospin-1/2 Dirac-like cones.…”

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confidence: 87%

“…Interestingly, the notion of the square root operation can also be extended to HOTIs, where the emergence of paired in-gap corner states in square-root HOTIs was found to be mediated by higher-order topology of the parent Hamiltonian. − So far, however, the square-root HOTIs have been experimentally demonstrated in electric circuits and acoustic structures, − but not in photonics, which offers a new scheme for robust light guiding and trapping. Moreover, it is worth noting that the concept of square-root topology has been extended to 2 n -root topological insulators, topological semimetals, and other HOTI creatures. , …”

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confidence: 99%

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Realization of Second-Order Photonic Square-Root Topological Insulators

et al. 2021

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Square-root higher-order topological insulators (HOTIs) are recently discovered new topological phases, with intriguing topological properties inherited from a parent lattice Hamiltonian. Different from conventional HOTIs, the square-root HOTIs typically manifest two paired nonzero energy corner states. In this work, we experimentally demonstrate the second-order square-root HOTIs in photonics for the first time to our knowledge, thereby unveiling such distinct corner states. The specific platform is a laser-written decorated honeycomb lattice (HCL), for which the squared Hamiltonian represents a direct sum of the underlying HCL and breathing Kagome lattice. The localized corner states residing in different bandgaps are observed with characteristic phase structures, in sharp contrast to the discrete diffraction in a topologically trivial structure. Our work illustrates a scheme to study fundamental topological phenomena in systems with the coexistence of spin-1/2 and spin-1 Dirac-Weyl Fermions and may bring about new possibilities in topology-driven photonic devices.

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confidence: 87%

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confidence: 99%

Realization of Second-Order Photonic Square-Root Topological Insulators

et al. 2021

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“…Recently, square-root topological phase is discovered as a new class of matter [25], whose topological properties are inherited from its squared parent model through a process analogous to the transition from Klein-Gordon [26,27] to Dirac equations [28] in relativistic quantum mechanics. In-gap topological edge modes are found in tight-binding models of square-root topological insulators, superconductors and semimetals [29][30][31][32][33][34][35][36][37][38][39][40][41]. Moreover, general rules of constructing 2 n th-root topological phases [35][36][37] and symmetry-based classifications of these intriguing states [38] are proposed.…”

Section: Introductionmentioning

confidence: 99%

“…In-gap topological edge modes are found in tight-binding models of square-root topological insulators, superconductors and semimetals [29][30][31][32][33][34][35][36][37][38][39][40][41]. Moreover, general rules of constructing 2 n th-root topological phases [35][36][37] and symmetry-based classifications of these intriguing states [38] are proposed. Experimental evidence of square-root topological phases has also been reported in photonic [30], electric [31] and acoustic [32] systems.…”

Section: Introductionmentioning

confidence: 99%

$q$th-root non-Hermitian Floquet topological insulators

Zhou,

Bomantara,

2022

Preprint

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Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer qth-root of the evolution operator U that describes Floquet topological matter. As a case study, we apply our qth-rooting procedure to obtain the square-and cubic-root firstand second-order non-Hermitian Floquet topological insulators. There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies π/2, π/3 and 2π/3, whose numbers can be large and are highly controllable. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. By repeatedly applying the square-and cubic-rooting procedure, the resulting 2 n th-and 3 n th-root systems are found to possess degenerate edge or corner modes at quasienergies ±(0, 1, ...2 n )π/2 n and ±(0, 1, ..., 3 n )π/3 n , respectively, whose numbers are determined by the bulk topological invariants of the parent system U . Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet systems.

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“…The square-root TI was subsequently observed in a photonic cage [5]. Recently, the square-root operation has been applied to higher-order topological insulators (HOTIs) that allow topologically robust edge states with codimension larger than one [6][7][8][9][10][11][12][13][14][15]. Besides the gapped solution, e.g., the electron-positron pair, the Dirac equation allows another crucial gapless or massless solution called Weyl fermion [16] that plays an important role in quantum field theory and the Standard Model.…”

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confidence: 99%