Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

Vyas, Vivek M.; Roy, Dibyendu

doi:10.1103/physrevb.103.075441

Cited by 32 publications

(10 citation statements)

References 48 publications

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“…Originally formulated in the context of anomalies, they revolutionized the field of condensed matter physics in the form of topological insulators and semimetals 1 – 3 . More recently, they aroused much attention again as non-Hermitian skin states, which demonstrated how unbalanced non-Hermitian gain/loss can challenge well-held tenets of bulk-boundary correspondence 4 – 19 .…”

Section: Introductionmentioning

confidence: 99%

Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

et al. 2021

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Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness—topological protection, as well as the non-Hermitian skin effect. In this work, we report the experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.

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Section: Introductionmentioning

confidence: 99%

Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

et al. 2021

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“…The relevance and importance of geometric phase in classical mechanical systems also received significant attention [16][17][18][19][20][21], as also in the context of particle physics [22][23][24][25]. The importance of geometric phase in understanding condensed matter systems was noted immediately after Berry's work [7,22,[25][26][27] and forms the pillar of the current understanding of the physics of topological materials and quantum Hall effect, as also that of exotic objects like anyons [2,[28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Generalised Geometric Phase

Vyas¹

2023

Preprint

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A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the argument of the matrix element of an observable as a generalised relative phase. This identification naturally paves the way for defining an operator generalisation of the geometric phase following Pancharatnam. The notion of natural connection finds an appropriate operator generalisation, and the generalised geometric phase is indeed found to be the (an)holonomy of the generalised connection. It is shown that in scenarios wherein the usual geometric phase is not defined, the generalised geometric phase manifests as a global phase acquired by a quantum state in course of time evolution. The generalised geometric phase is found to contribute to the shift in the energy spectrum due perturbation, and to the forward scattering amplitude in a scattering problem.

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“…In the presence of gain and loss or nonreciprocal effects, unique topological phenomena without any counterparts in closed systems could emerge, such as the non-Hermitian skin effect (NHSE) [51][52][53][54][55][56][57] and exceptional topological phases [50]. The interplay between time-periodic drivings and non-Hermitian effects could further induce intriguing phases in out-of-equilibrium situations, like the non-Hermitian Floquet topological insulators [58][59][60][61][62][63][64][65][66][67][68][69], superconductors [70,71], semimetals [72][73][74][75] and quasicrystals [76][77][78]. As reported in this paper, applying our qth-rooting procedure to such non-Hermitian Floquet phases yields even more exotic features absent in their original counterparts, such as fractionalquasienergy topological edge and corner modes.…”

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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Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

Cited by 32 publications

References 48 publications

Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

Generalised Geometric Phase

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

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