Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Yokomizo, Kazuki; Murakami, Shuichi

doi:10.1103/physrevresearch.2.043045

Cited by 53 publications

(23 citation statements)

References 129 publications

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“…This previous work showed a critical non-Hermitian skin effect, where an energy spectrum and localization of eigenstates discontinuously jump across a critical point. We note that since the critical non-Hermitian skin effect occurs in the thermodynamic limit, this effect can be systematically understood in terms of a non-Bloch band theory [4,24,[29][30][31][32][33][34]. This is because in non-Hermitian systems with open boundary conditions, the non-Bloch band theory can calculate continuum energy bands in the limit of a large system size.…”

Section: Introductionmentioning

confidence: 99%

Scaling rule in critical non-Hermitian skin effect

Yokomizo,

Murakami

2021

Preprint

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Non-Hermitian systems show a non-Hermitian skin effect, where the bulk states are localized at a boundary of the systems with open boundary conditions. In this paper, we study dependence of the localization length of the eigenstates on a system size in a specific non-Hermitian model with a critical non-Hermitian skin effect, where the energy spectrum undergoes discontinuous transition in the thermodynamic limit. We analytically show that the eigenstates exhibit remarkable localization, known as scale-free localization, where the localization length is proportional to a system size. Our result gives a theoretical support for the scale-free localization, which has been proposed only numerically in previous works.

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Section: Introductionmentioning

confidence: 99%

Scaling rule in critical non-Hermitian skin effect

Yokomizo,

Murakami

2021

Preprint

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“…Symmetry classes are enriched in non-Hermitian systems because transposition and complex conjugation for the Hamiltonians are inequivalent 3 . Accordingly, various symmetry-protected skin effects 37,[68][69][70][71][72] and exceptional nodes 49,60,[73][74][75][76][77] has been theoretically suggested. Meanwhile, crystal symmetries give constraints on band structures.…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian band topology with generalized inversion symmetry

Okugawa,

Takahashi,

Yokomizo

2021

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Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. The generalization is unique to non-Hermitian systems. We show that parities of the winding numbers can be determined from energy eigenvalues on the inversion-invariant momenta when generalized inversion symmetry is present. The simple expressions for the winding numbers allow us to easily analyze skin effects and exceptional points in non-Hermitian bands. We also demonstrate the methods for (second-order) skin effects and exceptional points by using lattice models.

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“…In non-Hermitian crystals, this effect leads to localization of bulk eigenstates at boundaries of the systems with open boundary conditions [19][20][21][22][23][24][25]. Accordingly, the non-Hermitian skin effect have rich physics, and phenomena caused by this effect are unique to non-Hermitian systems [26][27][28][29]. In fact, the non-Hermitian skin effect was experimentally realized in various physical systems [30][31][32][33][34][35][36][37][38][39].…”

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confidence: 99%

Non-Hermitian waves in a continuous periodic model and application to photonic crystals

Yokomizo,

Yoda,

Murakami

2021

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In non-Hermitian systems, the eigenstates in the bulk are localized at the boundaries of the systems. It is called the non-Hermitian skin effect, and it has been studied mostly in discrete systems. In the present work, we study the non-Hermitian skin effect in a continuous periodic model. In a one-dimensional system, we show that the localization length are equal for all the eigenstates. Moreover, the localization length and the eigenspectra in a large system are independent of the types of open boundary conditions. These properties are also found in a non-Hermitian photonic crystal. Such remarkable behaviors in a continuous periodic model can be explained in terms of the non-Bloch band theory. By constructing the generalized Brillouin zone for a complex Bloch wave number, we derive the localization length and the eigenspectra under an open boundary condition. Furthermore we show that the generalized Brillouin zone also gives various physical properties, such as bulk-edge correspondence.

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Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Cited by 53 publications

References 129 publications

Scaling rule in critical non-Hermitian skin effect

Scaling rule in critical non-Hermitian skin effect

Non-Hermitian band topology with generalized inversion symmetry

Non-Hermitian waves in a continuous periodic model and application to photonic crystals

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