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Anomalous Edge State in a Non-Hermitian Lattice
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TLDR
It is shown that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity and a one-dimensional tight-binding model with gain and loss as well as long-range hopping is considered.Abstract:
We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by a non-Hermitian Hamiltonian that encircles an exceptional point in momentum space. The winding number has a fractional value of 1/2. There is only one dynamically stable zero-energy edge state due to the defectiveness of the Hamiltonian. This edge state is robust to disorder due to protection by a chiral symmetry. We also discuss experimental realization with arrays of coupled resonator optical waveguides.read more
Citations
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Journal ArticleDOI
Topological Photonics
Tomoki Ozawa,Hannah M. Price,Alberto Amo,Nathan Goldman,Mohammad Hafezi,Ling Lu,Mikael C. Rechtsman,David Schuster,Jonathan Simon,Oded Zilberberg,Iacopo Carusotto +10 more
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Journal ArticleDOI
Edge States and Topological Invariants of Non-Hermitian Systems.
Shunyu Yao,Zhong Wang +1 more
TL;DR: This work obtains the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by theNon-Bloch winding number instead of the Bloch-Hamiltonian-based topological number.
Journal ArticleDOI
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems.
TL;DR: This work provides a comprehensive framework for generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
Journal ArticleDOI
Exceptional topology of non-Hermitian systems
TL;DR: In this paper, the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed.
Journal ArticleDOI
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems.
Daniel Leykam,Konstantin Y. Bliokh,Konstantin Y. Bliokh,Chunli Huang,Chunli Huang,Yidong Chong,Franco Nori,Franco Nori +7 more
TL;DR: Chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation are found to be divided into three families, characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points.
References
More filters
Journal ArticleDOI
Topological Photonics
Tomoki Ozawa,Hannah M. Price,Alberto Amo,Nathan Goldman,Mohammad Hafezi,Ling Lu,Mikael C. Rechtsman,David Schuster,Jonathan Simon,Oded Zilberberg,Iacopo Carusotto +10 more
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Journal ArticleDOI
Edge States and Topological Invariants of Non-Hermitian Systems.
Shunyu Yao,Zhong Wang +1 more
TL;DR: This work obtains the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by theNon-Bloch winding number instead of the Bloch-Hamiltonian-based topological number.
Journal ArticleDOI
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems.
TL;DR: This work provides a comprehensive framework for generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
Journal ArticleDOI
Exceptional topology of non-Hermitian systems
TL;DR: In this paper, the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed.
Journal ArticleDOI
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems.
Daniel Leykam,Konstantin Y. Bliokh,Konstantin Y. Bliokh,Chunli Huang,Chunli Huang,Yidong Chong,Franco Nori,Franco Nori +7 more
TL;DR: Chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation are found to be divided into three families, characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points.
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