Self-Healing of Non-Hermitian Topological Skin Modes

Article Multidisciplinary Sciences

Topological triple phase transition in non-Hermitian Floquet quasicrystals

Sebastian Weidemann et al.

Summary: Phase transitions in non-Hermitian quasicrystals can be mutually interlinked, and the intertwinement of symmetry breaking, topology, and mobility phase transitions is observed in this study using photonic quantum walks.

NATURE (2022)

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Article Physics, Multidisciplinary

Non-Hermitian Edge Burst

Wen-Tan Xue et al.

Summary: We have discovered an unexpected non-Hermitian phenomenon called "edge burst" in non-Hermitian quantum dynamics. This phenomenon occurs in a class of non-Hermitian quantum walk in periodic lattices with open boundary conditions, where a large portion of loss happens at the system boundary. The edge burst is caused by the interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. We have also established a universal bulk-edge scaling relation that explains the non-Hermitian edge burst, which can be experimentally observed in various non-Hermitian systems including quantum-optical and cold-atom platforms.

PHYSICAL REVIEW LETTERS (2022)

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Article Materials Science, Multidisciplinary

Connections between the open-boundary spectrum and the generalized Brillouin zone in non-Hermitian systems

Deguang Wu et al.

Summary: This paper investigates the connections between the periodic-boundary spectrum, open-boundary spectrum, and the generalized Brillouin zone in a one-dimensional non-Hermitian system. It proposes an efficient numerical method for accurately calculating these properties. Furthermore, the study extends these connections to non-Hermitian systems in the symplectic symmetry class.

PHYSICAL REVIEW B (2022)

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Article Physics, Multidisciplinary

Knots and Non-Hermitian Bloch Bands

Haiping Hu et al.

Summary: This study explores knots tied by eigenenergy strings in one-dimensional non-Hermitian Hamiltonians, as well as their relationship with Wilson loops. An algorithm is developed to construct corresponding tight-binding non-Hermitian Hamiltonians and a scheme is proposed to probe knot structures via quantum quench.

PHYSICAL REVIEW LETTERS (2021)

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Article Multidisciplinary Sciences

Topological complex-energy braiding of non-Hermitian bands

Kai Wang et al.

Summary: The recent theoretical work discovered that the braid group characterizes the topology of non-Hermitian periodic systems, where the complex band energies can braid in momentum space. This study introduces a tight-binding lattice model that can achieve arbitrary elements in the braid group of two strands B-2 and experimentally demonstrates topological complex-energy braiding of non-Hermitian bands in a synthetic dimension. The results provide a direct demonstration of the braid-group characterization of non-Hermitian topology and open a pathway for designing and realizing topologically robust phases in open classical and quantum systems.

NATURE (2021)

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Article Physics, Multidisciplinary

Detecting Non-Bloch Topological Invariants in Quantum Dynamics

Kunkun Wang et al.

Summary: Non-Bloch topological invariants have been dynamically detected in single-photon quantum walks, revealing their robustness against symmetry-preserving disorders and consistency with theoretical predictions. The experiments performed far from boundaries highlight these invariants as intrinsic properties of the system persisting in the thermodynamic limit, shedding new light on experimental investigation of non-Hermitian topology.

PHYSICAL REVIEW LETTERS (2021)

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Review Physics, Multidisciplinary

Exceptional topology of non-Hermitian systems

Emil J. Bergholtz et al.

Summary: This review discusses the current understanding of the role of topology in non-Hermitian systems and its physical consequences in dissipative settings, focusing on the concept of exceptional degeneracies and its distinct phenomena, as well as the new notions of gapped phases in single-band systems. The unique sensitivity of non-Hermitian matrices to boundary conditions is highlighted, leading to anomalous relationships between bulk and boundary physics. Additionally, applications of non-Hermitian topology in classical and quantum systems are reviewed, showing its relevance beyond the field of topological phases.

REVIEWS OF MODERN PHYSICS (2021)

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Article Physics, Multidisciplinary

Non-Hermitian Skin Effects in Hermitian Correlated or Disordered Systems: Quantities Sensitive or Insensitive to Boundary Effects and Pseudo-Quantum-Number

Nobuyuki Okuma et al.

Summary: In the condensed matter community, there is a common belief that bulk quantities become insensitive to boundary conditions in the infinite-volume limit. However, recent research has shown that for non-Hermitian Hamiltonians, spectra strongly depend on boundary conditions, which can have significant effects in Hermitian correlated or disordered systems. Additionally, non-normal pseudospectra can be tested through sharp optical absorption, indicating the emergence of pseudo quantum numbers as a result of high non-normality.

PHYSICAL REVIEW LETTERS (2021)

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Article Multidisciplinary Sciences

Generating arbitrary topological windings of a non-Hermitian band

Kai Wang et al.

Summary: The nontrivial topological features of non-Hermitian systems can be experimentally demonstrated and controlled by changing modulation waveforms. This topological winding allows for the synthesis and characterization of nontrivial phases in nonconservative systems.

SCIENCE (2021)

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Article Optics

Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation

Stefano Longhi

Summary: This study discusses the topological phase transition of optical superlattices with sublattice symmetry under a synthetic imaginary gauge field, described by the change of a spectral winding number. The phase transition for a narrow gap is of universal form and can be described by a non-Hermitian Dirac equation.

OPTICS LETTERS (2021)

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Article Optics

Steering non-Hermitian skin modes by synthetic gauge fields in optical ring resonators

Zekun Lin et al.

Summary: This study demonstrates a versatile approach to generate and control the non-Hermitian skin effect for photons using synthetic gauge fields. By utilizing indirectly coupled optical ring resonator arrays with long-range couplings and on-site gain and loss, the researchers have validated the appearance of the skin effect under certain conditions and explored its properties and potential applications in propagation effects.

OPTICS LETTERS (2021)

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Article Physics, Multidisciplinary

Exact Solution of Non-Hermitian Systems with Generalized Boundary Conditions: Size-Dependent Boundary Effect and Fragility of the Skin Effect

Cui-Xian Guo et al.

Summary: The study reveals the sensitivity of systems with non-Hermitian skin effects to boundary conditions and lattice size. In one-dimensional non-Hermitian models, the existence of non-Hermitian skin effects is identified even when one of the boundary hopping terms vanishes. However, it is shown that in the thermodynamic limit, this skin effect is fragile to any tiny boundary perturbations.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary

Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions

Heinrich-Gregor Zirnstein et al.

Summary: This study investigates the realization of genuinely non-Hermitian topological phases in open systems with strong gain and loss, and reveals that the non-Hermitian winding number in one dimension indicates a topological phase transition in the bulk, implying spatial growth of the bulk Green function.

PHYSICAL REVIEW LETTERS (2021)

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Article Physics, Multidisciplinary

Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing

Taiki Haga et al.

Summary: The study shows that the longest relaxation time in a quantum dissipative system depends on both the Liouvillian gap and the localization length of the eigenmodes. The longest relaxation time can diverge as the system size increases, even without the gap closing.

PHYSICAL REVIEW LETTERS (2021)

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Article Materials Science, Multidisciplinary

Non-Hermitian skin effect beyond the tight-binding models

Stefano Longhi

Summary: The energy bands of non-Hermitian systems have nontrivial topological features that result from the complex nature of the energy spectrum, characterized by integer nonzero winding numbers. The nontrivial winding provides the topological signature of the non-Hermitian skin effect (NHSE) at lattice edges under open boundary conditions. While most current results rely on tight-binding models of non-Hermitian systems, exact Bloch wave function analysis of the NHSE and related topological band theory is still lacking.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Non-Hermitian band topology with generalized inversion symmetry

Ryo Okugawa et al.

Summary: By generalizing inversion symmetry, this study provides a method to detect skin effects and exceptional points in non-Hermitian systems. The parity of winding numbers can be determined from energy eigenvalues on inversion-invariant momenta in the presence of generalized inversion symmetry. The simple expressions for winding numbers facilitate the analysis of skin effects and exceptional points in non-Hermitian bands.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems

Kazuki Yokomizo et al.

Summary: Recent research shows non-Hermitian systems are sensitive to boundaries, with the construction of non-Bloch band theory in bosonic BdG systems revealing rich non-Hermitian aspects such as instability against perturbations and reentrant behavior. This theory proves to be a powerful tool for studying non-Hermitian nature in bosonic BdG systems.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Skin effect and winding number in disordered non-Hermitian systems

Jahan Claes et al.

Summary: This paper discusses the non-Hermitian skin effect, extends the definition of the winding number to disordered NH systems, and verifies that the real-space formula can still predict the NH skin effect.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems

Nobuyuki Okuma et al.

Summary: This study explores the roles of non-Hermitian topology in the spectral properties and entanglement structures of open systems, providing a unified understanding of quantum anomaly and non-Hermitian skin effects. By using this unified interpretation, symmetry-protected and higher-dimensional skin effects are classified. In terms of entanglement structure, the steady states of fermionic open systems with non-Hermitian topological spectra are investigated, linking them to Majorana edge modes and chiral edge states.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Non-Hermitian second-order skin and topological modes

Yongxu Fu et al.

Summary: The paper investigates second-order corner modes in non-Hermitian systems using a nested tight-binding formalism, providing an accurate description of corner modes and hybrid skin-topological corner modes for the four-band model. By validating and illustrating the results with specific examples, the proposed method proves to be effective in capturing the corner modes induced by second-order skin effect.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Scaling rule for the critical non-Hermitian skin effect

Kazuki Yokomizo et al.

Summary: This study explores the dependence of the localization length of eigenstates on system size in a specific non-Hermitian model with critical non-Hermitian skin effect. It analytically demonstrates the remarkable scale-free localization behavior of eigenstates in this model.

PHYSICAL REVIEW B (2021)

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Article Physics, Multidisciplinary

Non-Bloch-Band Collapse and Chiral Zener Tunneling

S. Longhi

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Non-Hermitian Boundary Modes and Topology

Dan S. Borgnia et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Topological Origin of Non-Hermitian Skin Effects

Nobuyuki Okuma et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Multidisciplinary Sciences

Topological funneling of light

Sebastian Weidemann et al.

SCIENCE (2020)

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Article Physics, Multidisciplinary

Non-Hermitian bulk-boundary correspondence in quantum dynamics

Lei Xiao et al.

NATURE PHYSICS (2020)

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Article Physics, Multidisciplinary

Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits

T. Helbig et al.

NATURE PHYSICS (2020)

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Article Physics, Multidisciplinary

Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems

Kai Zhang et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Ching Hua Lee et al.

COMMUNICATIONS PHYSICS (2020)

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Article Physics, Multidisciplinary

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

Zhesen Yang et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

Norifumi Matsumoto et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Applied

Two-dimensional non-Hermitian Skin Effect in a Synthetic Photonic Lattice

Yiling Song et al.

PHYSICAL REVIEW APPLIED (2020)

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Review Physics, Condensed Matter

Non-Hermitian physics

Yuto Ashida et al.

ADVANCES IN PHYSICS (2020)

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Article Physics, Multidisciplinary

Helical damping and dynamical critical skin effect in open quantum systems

Chun-Hui Liu et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Physics, Multidisciplinary

Phase transitions and generalized biorthogonal polarization in non-Hermitian systems

Elisabet Edvardsson et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Physics, Multidisciplinary

Reciprocal skin effect and its realization in a topolectrical circuit

Tobias Hofmann et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Materials Science, Multidisciplinary

Second-order topological non-Hermitian skin effects

Ryo Okugawa et al.

PHYSICAL REVIEW B (2020)

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Article Multidisciplinary Sciences

Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial

Ananya Ghatak et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2020)

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Article Multidisciplinary Sciences

Critical non-Hermitian skin effect

Linhu Li et al.

NATURE COMMUNICATIONS (2020)

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Article Materials Science, Multidisciplinary

Higher-order non-Hermitian skin effect

Kohei Kawabata et al.

PHYSICAL REVIEW B (2020)

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Article Physics, Multidisciplinary

Anomalous Topological Edge States in Non-Hermitian Piezophononic Media

Penglin Gao et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Non-Hermitian Skin Modes Induced by On-Site Dissipations and Chiral Tunneling Effect

Yifei Yi et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Materials Science, Multidisciplinary

Unraveling the non-Hermitian skin effect in dissipative systems

Stefano Longhi

PHYSICAL REVIEW B (2020)

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Article Materials Science, Multidisciplinary

Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect

Xizheng Zhang et al.

PHYSICAL REVIEW B (2020)

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Article Materials Science, Multidisciplinary

Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class

Kohei Kawabata et al.

PHYSICAL REVIEW B (2020)

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Article Materials Science, Multidisciplinary

Perspective on topological states of non-Hermitian lattices

Luis E. F. Foa Torres

JOURNAL OF PHYSICS-MATERIALS (2020)

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Review Physics, Condensed Matter

New topological invariants in non-Hermitian systems

Ananya Ghatak et al.

JOURNAL OF PHYSICS-CONDENSED MATTER (2019)

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Article Physics, Multidisciplinary

Second-Order Topological Phases in Non-Hermitian Systems

Tao Liu et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Hybrid Higher-Order Skin-Topological Modes in Nonreciprocal Systems

Ching Hua Lee et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Topological Phase Transition in non-Hermitian Quasicrystals

S. Longhi

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Topological Phase Transition Driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics

Nobuyuki Okuma et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Non-Bloch Band Theory of Non-Hermitian Systems

Kazuki Yokomizo et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Optics

Non-Bloch PT symmetry breaking in non-Hermitian photonic quantum walks

Stefano Longhi

OPTICS LETTERS (2019)

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Article Physics, Multidisciplinary

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems

Fei Song et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics

Jong Yeon Lee et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Symmetry and Topology in Non-Hermitian Physics

Kohei Kawabata et al.

PHYSICAL REVIEW X (2019)

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Article Physics, Applied

Demonstration of self-healing and scattering resilience of acoustic Bessel beams

Giuseppe Antonacci et al.

APPLIED PHYSICS LETTERS (2019)

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Article Physics, Multidisciplinary

Non-Hermitian Topological Invariants in Real Space

Fei Song et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Materials Science, Multidisciplinary

Generalized bulk-edge correspondence for non-Hermitian topological systems

Ken-Ichiro Imura et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence

Elisabet Edvardsson et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry

L. Jin et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Periodic table for topological bands with non-Hermitian symmetries

Hengyun Zhou et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Non-Hermitian systems and topology: A transfer-matrix perspective

Flore K. Kunst et al.

PHYSICAL REVIEW B (2019)

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Article Optics

Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition

Loic Herviou et al.

PHYSICAL REVIEW A (2019)

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Article Materials Science, Multidisciplinary

Anatomy of skin modes and topology in non-Hermitian systems

Ching Hua Lee et al.

PHYSICAL REVIEW B (2019)

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Article Physics, Multidisciplinary

Probing non-Hermitian skin effect and non-Bloch phase transitions

Stefano Longhi

PHYSICAL REVIEW RESEARCH (2019)

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Article Materials Science, Multidisciplinary

Topological phase transition independent of system non-Hermiticity

K. L. Zhang et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Topological classification of non-Hermitian systems with reflection symmetry

Chun-Hui Liu et al.

PHYSICAL REVIEW B (2019)

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Article Physics, Multidisciplinary

Topological Band Theory for Non-Hermitian Hamiltonians

Huitao Shen et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems

Flore K. Kunst et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Edge States and Topological Invariants of Non-Hermitian Systems

Shunyu Yao et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Non-Hermitian Chern Bands

Shunyu Yao et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Topological Phases of Non-Hermitian Systems

Zongping Gong et al.

PHYSICAL REVIEW X (2018)

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Article Physics, Multidisciplinary

Multiple self-healing Bloch surface wave beams generated by a two-dimensional fraxicon

Myun-Sik Kim et al.

COMMUNICATIONS PHYSICS (2018)

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Article Materials Science, Multidisciplinary

Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points

V. M. Martinez Alvarez et al.

PHYSICAL REVIEW B (2018)

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Article Physics, Multidisciplinary

Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems

Daniel Leykam et al.

PHYSICAL REVIEW LETTERS (2017)

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Article Physics, Multidisciplinary

Self-acceleration in non-Hermitian systems

C. Yuce et al.

PHYSICS LETTERS A (2017)

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Article Chemistry, Multidisciplinary

Diffraction-Free Bloch Surface Waves

Ruxue Wang et al.

ACS NANO (2017)

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Article Physics, Multidisciplinary

Anomalous Edge State in a Non-Hermitian Lattice

Tony E. Lee

PHYSICAL REVIEW LETTERS (2016)

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Article Physics, Applied

Acoustic non-diffracting Airy beam

Zhou Lin et al.

JOURNAL OF APPLIED PHYSICS (2015)

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Propagation Dynamics of Airy Water-Wave Pulses

Shenhe Fu et al.

PHYSICAL REVIEW LETTERS (2015)

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Article Optics

Isotropic three-dimensional super-resolution imaging with a self-bending point spread function

Shu Jia et al.

NATURE PHOTONICS (2014)

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Article Multidisciplinary Sciences

Generation of acoustic self-bending and bottle beams by phase engineering

Peng Zhang et al.

NATURE COMMUNICATIONS (2014)

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Self-healing of quantum entanglement after an obstruction

Melanie McLaren et al.

NATURE COMMUNICATIONS (2014)

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Generation of Nondiffracting Electron Bessel Beams

Vincenzo Grillo et al.

PHYSICAL REVIEW X (2014)

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Article Multidisciplinary Sciences

Generation of electron Airy beams

Noa Voloch-Bloch et al.

NATURE (2013)

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Review Optics

Bessel and annular beams for materials processing

Marti Duocastella et al.

LASER & PHOTONICS REVIEWS (2012)

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Article Physics, Multidisciplinary

Cosine-Gauss Plasmon Beam: A Localized Long-Range Nondiffracting Surface Wave

Jiao Lin et al.

PHYSICAL REVIEW LETTERS (2012)

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Nonparaxial Mathieu and Weber Accelerating Beams

Peng Zhang et al.

PHYSICAL REVIEW LETTERS (2012)

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Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination

Thomas A. Planchon et al.

NATURE METHODS (2011)

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Microscopy with self-reconstructing beams

Florian O. Fahrbach et al.

NATURE PHOTONICS (2010)

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Nonlinear generation and manipulation of Airy beams

Tal Ellenbogen et al.

NATURE PHOTONICS (2009)

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Optically mediated particle clearing using Airy wavepackets

Joerg Baumgartl et al.

NATURE PHOTONICS (2008)

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Self-healing properties of optical Airy beams

John Broky et al.

OPTICS EXPRESS (2008)

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Observation of accelerating airy beams

G. A. Siviloglou et al.

PHYSICAL REVIEW LETTERS (2007)

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Review Physics, Multidisciplinary

Bessel beams: diffraction in a new light

D McGloin et al.

CONTEMPORARY PHYSICS (2005)

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Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam

V Garcés-Chávez et al.

NATURE (2002)

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Self-Healing of Non-Hermitian Topological Skin Modes

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