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arXiv · 2412.05809

Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry

Yifan Wang·Wladimir A. Benalcazar
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Abstract

In two dimensions, Hermitian lattices with non-zero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen-Ninomiya no-go theorem at their one-dimensional boundaries. This allows the realization of topologically-protected one-dimensional edges with nonreciprocal dynamics. However, unlike the edge states of Chern insulators, the nonreciprocal edges of HOSE phases exist only at certain edges of the two-dimensional lattice, not all, leading to corner-localized states. In this paper, we investigate the topological connections between these two systems and uncover novel non-Hermitian topological phases possessing higher-order topological knots (HOTKs). These phases arise from multiband topology protected by crystalline symmetries and host nonreciprocal edge states that circulate the entire boundary of the two-dimensional lattice. We show that phase transitions typically separate HOTK phases from complex Chern insulator phases - non-Hermitian lattices with nonzero Chern numbers protected by imaginary line gaps in the presence of time-reversal symmetry.

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Yifan Wang, Wladimir A. Benalcazar. 2024-12-08. Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry. https://doi.org/10.1103/physrevb.111.205123

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