Anomalous Edge State in a Non-Hermitian Lattice.
TLDR
In this paper, the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity, and the authors consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping.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
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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.
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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.
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Topological Band Theory for Non-Hermitian Hamiltonians.
TL;DR: The topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex, is developed and "gapped" bands in one and two dimensions are classified by explicitly finding their topological invariants.
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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.