Edge States and Topological Invariants of Non-Hermitian Systems.

By Shunyu Yao, Zhong Wang. Physical Review Letters, 2018

1,698 citations recorded by the source corpus.

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/751fdbf1e1c527e8744760ac147c4f1fe56f6303

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Experimental realization of a Weyl exceptional ring (2018, background): “[56] Shunyu Yao and Zhong Wang, “Edge States and”
Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “, the nonreciprocal Su-Schrieffer-Heeger model [48, 49, 51, 53].”
Roadmap on topological photonics (2022, positive): “The non-Hermitian skin effect, where non-hermiticity appears due to non-reciprocity, yields an extensive localization of bulk modes at the edge, challenging the conventional view of topological bulk-boundary correspondence [109].”
Perspective on topological states of non-Hermitian lattices (2019, background): “tional points with an order scaling with the system size in Ref. [46], an effect which was interpreted as an environment mediated interaction effect. The same effect was conﬁrmed analytically in Ref. [47] for a non-Hermitian SSH model with asymmetric Perspective on topological states of non-Hermitia”
A review on non-Hermitian skin effect (2022, methodology): “This theory takes a complex wave vector k0 ¼ k ilnr (it is in this form for the sake of concise formulism, with r some real values) to replace the initial real wave vector k and defines the GBZ based on k0 so that the nonHermitian dynamics can be characterized as the non-Bloch wave propagation gover”
Reciprocal skin effect and its realization in a topolectrical circuit (2019, background): “[16] S.”
Non-Hermitian systems and topology: A transfer-matrix perspective (2018, methodology): “Various topological invariants have been defined using a generalization of the conventional Berry connection by replacing the standard inner product with a biorthogonal one [52–56], but they often fail to predict the existence of robust boundary modes [50, 56–58].”
Non-Hermitian Chern Bands. (2018, positive): “The dissimilarity between open-boundary and Bloch spectra has also been found in a 1D model [46,53,54,56], whose spectra can be readily obtained via a similarity transformation to a Hermitian Hamiltonian [56].”