Hermitian Topologies originating from non-Hermitian braidings

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.

10 pages, 9 figures. Published in Phys. Rev. B

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Cited by in corpus (9)

• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Revealing the spatial nature of sublattice symmetry
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Nodal Spectral Functions Stabilized by Non-Hermitian Topology of Quasiparticles
• Emergence of Hermitian topology from non-Hermitian knots