Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits

Helbig, Tobias; Hofmann, Tobias; Imhof, Stefan; Abdelghany, Mohamed; Kießling, T.; Molenkamp, Laurens W.; Lee, C. H.; Szameit, Alexander; Greiter, Martin; Thomale, Ronny

doi:10.1038/s41567-020-0922-9

Cited by 759 publications

(453 citation statements)

References 22 publications

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“…Unlike previous works [28,29,39], we shall be primarily concerned with non-Hermitian NKMs not perturbatively connected to known Hermitian analogs. Despite their sophistication, these NKMs exhibit short-ranged tightbinding representations potentially realizable in disordered semimetals and non-reciprocal electrical or photonic circuits [40][41][42][43][44][45][46][47][48][49]. In particular, we illustrate how the topological tidal surface states can be mapped out as topolectrical resonances in non-Hermitian circuit realizations, based on recent experimental demonstrations involving analogous 1D circuit arrays [47].…”

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confidence: 99%

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Lee

Li²,

Liu

et al. 2020

Preprint

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The paradigm of metals has undergone a revision and diversification from the viewpoint of topology. Non-Hermitian nodal knot metals (NKMs) constitute a class of matter without Hermitian analog, where the intricate structure of complex-valued energy bands gives rise to knotted lines of exceptional points and new topological surface state phenomena. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their underlying parent knots, and complement our results by an optimized constructive ansatz that provides tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. In particular, we identify the surface state boundaries as ``tidal' intersections of the complex band structure in a marine landscape analogy. We further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

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confidence: 99%

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Lee

Li²,

Liu

et al. 2020

Preprint

Self Cite

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“…Theoretically, a wide range of non-Hermitian topological phases and phenomena have been classified and characterized according to their symmetries [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ] and dynamical signatures [ 18 , 19 , 20 , 21 , 22 , 23 ]. Experimentally, non-Hermitian topological matter have also been realized in cold atom [ 24 , 25 ], photonic [ 26 , 27 , 28 , 29 ], acoustic [ 30 , 31 , 32 ], electrical circuit [ 33 , 34 , 35 ] systems, and nitrogen-vacancy-center in diamond [ 36 ], leading to potential applications such as topological lasers [ 37 , 38 , 39 ] and high-performance sensors [ 40 , 41 , 42 , 43 ]. Additionally, non-Hermitian structures could also arise in supersymmetric quantum mechanics, where a series of supersymmetric models have been solved exactly [ 44 , 45 , 46 , 47 , 48 ].…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Zhou

2020

Entropy

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Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

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“…Notably, the existence of topological protection in non-Hermitian systems has led to the creation of a new research line which focuses on the development of so-called topological lasers [7,41,42]. In the light of these findings, and since standard topological invariants-such as the Chern number of the momentum-bulk Hamiltonian-may fail to correctly predict the existence of topological edge states in non-Hermitian systems [30,[43][44][45][46][47][48], many efforts are being devoted to investigate the benefits of the interplay between topology and PT symmetry [49][50][51][52][53]. Prominently, there is an ongoing quest to generalize the bulk-boundary correspondence for non-Hermitian systems [54][55][56], which has revealed new phenomena exclusive to such non-Hermitian topological systems [57,58].…”

Section: Introductionmentioning

confidence: 99%

Topological protection in non-Hermitian Haldane honeycomb lattices

Reséndiz-Vázquez

Tschernig

Pérez-Leija

et al. 2020

Phys. Rev. Research

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Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically protected edge states in non-Hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. Here we present a study of the emergence of topological edge states in two-dimensional Haldane lattices exhibiting balanced gain and loss. In line with recent studies on other Chern insulator models, we show that edge states can be observed in the so-called broken PT-symmetric phase, that is, when the spectrum of the gain-loss-balanced system's Hamiltonian is not entirely real. More importantly, we find that such topologically protected edge states emerge irrespective of the lattice boundaries, namely, zigzag, bearded, or armchair.

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Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits

Cited by 759 publications

References 22 publications

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Topological protection in non-Hermitian Haldane honeycomb lattices

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