Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory

Yang, Zhesen; Zhang, Kai; Fang, Chen; Hu, Jiangping

doi:10.1103/physrevlett.125.226402

Cited by 389 publications

(213 citation statements)

References 56 publications

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“…Next, let us consider a long chain. For the bulk eigenstates, two roots out of the four roots are required to satisfy the condition [91,92]: |β 2 | = |β 3 | = β, leading to the constraint ξ = 0. Considering the limit E → ± √ 2t 2 , we get physically feasible solutions as −γ m x γ corresponding to the edge states.…”

Section: Bulk-boundary Correspondencementioning

confidence: 99%

Non-Hermitian semi-Dirac semi-metals

Banerjee

Narayan

2021

J. Phys.: Condens. Matter

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Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest.In this work we propose the non-Hermitian generalization of semi-Dirac semimetals, which feature a linear dispersion along one momentum direction and a quadratic one along the other. We study the topological phase transitions in such two-dimensional semi-Dirac semimetals in the presence of a particle gain-and-loss term. We show that such a non-Hermitian term creates exceptional points (EPs) originating out of each semi-Dirac point. We map out the topological phase diagram of our model, using winding number and vorticity as topological invariants of the system. By means of numerical and analytical calculations, we examine the nature of edge states for different types of semi-Dirac models and establish bulk-boundary correspondence and absence of the non-Hermitian skin effect, in one class. On the other hand, for other classes of semi-Dirac models with asymmetric hopping, we restore the non-Hermitian skin effect, an anomalous feature usually present in non-Hermitian topological systems.

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Section: Bulk-boundary Correspondencementioning

confidence: 99%

Non-Hermitian semi-Dirac semi-metals

Banerjee

Narayan

2021

J. Phys.: Condens. Matter

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“…Here because of the factor e −β in Eqs. (34) and Eq. (35), the replacement of the discrete sum by the loop integral is always valid by assuming a sufficiently large N , i.e., regardless of whether β is assumed to be fixed or assumed to scale linearly with N .…”

Section: Directional Signal Amplification Versus the Pbc-obc Spectralmentioning

confidence: 99%

Quantized classical response from spectral winding topology

Lee

et al. 2021

Preprint

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Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge modes as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Speciﬁcally, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary ﬂux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

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“…Skin effect [13][14][15][16][17][18][19][20][21], a phenomenon unique to the non-Hermitian band theory, refers to the localization of eigenstates at the boundary, the number of which scales with the volume of the system. For example, in one dimension, all eigenstates of a non-Hermitian hamiltonian can be localized at the ends of a chain [13].…”

Section: Introductionmentioning

confidence: 99%

Universal non-Hermitian skin effect in two and higher dimensions

Zhang

Yang

Fang

2021

Preprint

Self Cite

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Skin effect, experimentally discovered in one dimension, describes the physical phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian hamiltonian are localized at the end(s) of the chain. Here in two and higher dimensions, we establish a theorem that the skin effect exists, if and only if periodic-boundary spectrum of the hamiltonian covers a finite area on the complex plane. This theorem establishes the universality of the effect, because the above condition is satisfied in almost every generic non-Hermitian hamiltonian, and, unlike in one dimension, is compatible with all spatial symmetries. We propose two new types of skin effect in two and higher dimensions: the corner-skin effect where all eigenstates are localized at one corner of the system, and the geometry-dependent-skin effect where skin modes disappear for systems of a particular shape, but appear on generic polygons. An immediate corollary of our theorem is that any non-Hermitian system having exceptional points (lines) in two (three) dimensions exhibits skin effect, making this phenomenon accessible to experiments in photonic crystals, Weyl semimetals, and Kondo insulators.

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Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory

Cited by 389 publications

References 56 publications

Non-Hermitian semi-Dirac semi-metals

Non-Hermitian semi-Dirac semi-metals

Quantized classical response from spectral winding topology

Universal non-Hermitian skin effect in two and higher dimensions

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