Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

By Chuanhao Yin, Hui Jiang, Linhu Li, R. Lu, Shu Chen. 2018

251 citations recorded by the source corpus.

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems being integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number of non-Hermitian system is equal to half of the summation of two winding numbers associated with two exceptional points respectively. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of zero-mode edge states is closely related to the winding number.

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

View Paper: https://www.semanticscholar.org/paper/9fd8d21d0f54b0b0afc43e188ede719a7a1e2c77

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Topological photonics (2018, background): “, 2011; Hu and Hughes, 2011), and what is its relevance to bulk-edge correspondence (some recent progress has been made in this direction (Kawabata et al., 2018b; Lee, 2016; Leykam et al., 2017a; Shen et al., 2018; Weimann et al., 2017; Yao et al., 2018; Yao and Wang, 2018; Yin et al., 2018))? In th”
Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “[118] C.”
Perspective on topological states of non-Hermitian lattices (2019, background): “hand, there is an intense activity in the search of a consistent classification [49, 50, 51, 52, 53], the definition of the topological invariants [54, 55, 56], and the search of a bulk-boundary correspondence [45, 46, 57, 58].”
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].”
Edge States and Topological Invariants of Non-Hermitian Systems. (2018, unknown): “[54] Chuanhao Yin, Hui Jiang, Linhu Li, Rong Lü, and Shu Chen, “Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral nonhermitian systems,” Phys.”
Symmetry-protected nodal phases in non-Hermitian systems (2018, background): “Very recently, intense theoretical [7–37] and experimental [38–45] efforts have been made to extend the concept of topological band structures to non-Hermitian (NH) systems which play an important role in the effective description of dissipation effects in various physi-”