Hermitian Topologies originating from non-Hermitian braidings
- URL: http://arxiv.org/abs/2212.13736v2
- Date: Fri, 6 Oct 2023 05:43:43 GMT
- Title: Hermitian Topologies originating from non-Hermitian braidings
- Authors: W. B. Rui, Y. X. Zhao, Z. D. Wang
- Abstract summary: We show that the complex energy bands of non-Hermitian systems braid in momentum space even in one dimension.
We derive an elegant identity that equates the linking number between the knots of braiding non-Hermitian bands and the zero-energy loop.
We construct typical topological phases with non-Hermitian braidings, which can be readily realized by artificial crystals.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The complex energy bands of non-Hermitian systems braid in momentum space
even in one dimension. Here, we reveal that the non-Hermitian braiding
underlies the Hermitian topological physics with chiral symmetry under a
general framework that unifies Hermitian and non-Hermitian systems.
Particularly, we derive an elegant identity that equates the linking number
between the knots of braiding non-Hermitian bands and the zero-energy loop to
the topological invariant of chiral-symmetric topological phases in one
dimension. Moreover, we find an exotic class of phase transitions arising from
the critical point transforming different knot structures of the non-Hermitian
braiding, which are not included in the conventional Hermitian topological
phase transition theory. Nevertheless, we show the bulk-boundary correspondence
between the bulk non-Hermitian braiding and boundary zero-modes of the
Hermitian topological insulators. Finally, we construct typical topological
phases with non-Hermitian braidings, which can be readily realized by
artificial crystals.
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