Square-root topological phase with time-reversal and particle-hole symmetry

Yoshida, Tsuneya; Mizoguchi, Tsuyoshi; Kuno, Yoshihito; Hatsugai, Yasuhiro

doi:10.1103/physrevb.103.235130

Cited by 19 publications

(9 citation statements)

References 45 publications

(54 reference statements)

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“…Recently, square-root topological phase is discovered [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 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 their symmetry classifications [38] are proposed.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Bomantara

2022

SciPost Phys.

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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 qqth-root of the evolution operator UU that describes Floquet topological matter. We further apply our qqth-rooting procedure to obtain 2^n2nth- and 3^n3nth-root first- and second-order non-Hermitian Floquet topological insulators~(FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies \pm(0,1,...2^{n})\pi/2^{n}±(0,1,...2n)π/2n and \pm(0,1,...,3^{n})\pi/3^{n}±(0,1,...,3n)π/3n, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

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Section: Introductionmentioning

confidence: 99%

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

Zhou

Bomantara

2022

SciPost Phys.

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show abstract

“…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.…”

mentioning

confidence: 99%