Anomalous features of non-Hermitian topological states

Yüce, C.

doi:10.1016/j.aop.2020.168098

Cited by 20 publications

(8 citation statements)

References 72 publications

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“…This implies that weak disorder can induce transition among the eigenstates clustered in the same group. This leads to the breakdown of chirality of topological states in 2D as dis-cussed by our earlier paper [35]. This is because of the fact that propagation of topological state is supported in only one direction in an Hermitian 2D strip, since no state is available at the same energy that propagates in the opposite direction on the same edge.…”

Section: Examplesmentioning

confidence: 90%

Eigenstate clustering around exceptional points

Yuce

2020

Preprint

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We propose an idea of eigenstate clustering in non-Hermitian systems. We show that nonorthogonal eigenstates can be clustered around exceptional points and illustrate our idea on some models. We discuss that exponential localization of eigenstates at edges due to the non-Hermitian skin effect is a typical example of eigenstate clustering. We numerically see that clustering of localized or extended eigenstates are possible in systems with both open and closed boundaries. We show that gain and loss can enhance eigenstate clustering. We use fidelities and the standard k-means clustering algorithm for a systematic study of clustered eigenstates.

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Section: Examplesmentioning

confidence: 90%

Eigenstate clustering around exceptional points

Yuce

2020

Preprint

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“…However, both of them as well as bulk eigenstates are localized around the left edge due to the non-Hermitian skin effect. In our recent paper [15], we showed that a zero-energy mode at the right edge can still be available, but it tends to move rapidly to the left edge.…”

Section: Non-topological Robust Zero-energy Edge Statesmentioning

confidence: 93%

Quasi-stationary solutions in non-Hermitian systems

Yuce

2021

Preprint

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Eigenstates exhibit localization at an open edge in a non-Hermitian lattice due to non-Hermitian skin effect. We here explore another interesting feature of non-Hermitian skin effect and predict quasi-stationary solutions, which are approximately time-independent. We show that the transition from such states to eigenstates is dramatically non-perturbative. We consider a non-Hermitian variant of the Su-Schrieffer-Heeger (SSH) model and predict non-topological but robust quasi-stationary zero energy modes.

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“…We show that the dispersion relations given in Eqs. (56), (57), (60), and (61) are valid even when |ρ 1 | < 1 < |ρ 2 | does not hold. In our system, the condition of 1 < |ρ 2 | widely holds but the condition of |ρ 1 | < 1 breaks down with increasing γ.…”

Section: Appendixmentioning

confidence: 99%

Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence

Takane

2022

Preprint

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A non-Hermitian Chern insulator with gain/loss-type non-Hermiticity shows a peculiar gap closing; when a nontrivial Chern insulator phase changes to a gapless phase, conduction and valence bands are combined into one band owing to destabilization of chiral edge states. A previous recipe of non-Hermitian bulkboundary correspondence is insufficient for this system since such a gap closing is beyond its scope. Here, we revise the recipe by taking the peculiar gap closing into account and apply it to the non-Hermitian Chern insulator. We demonstrate that the bulk-boundary correspondence holds in the system including a destabilization of chiral edge states. A phase diagram derived from the bulk-boundary correspondence is shown to be consistent with spectra of the system.

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Anomalous features of non-Hermitian topological states

Cited by 20 publications

References 72 publications

Eigenstate clustering around exceptional points

Eigenstate clustering around exceptional points

Quasi-stationary solutions in non-Hermitian systems

Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence

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