Topological phases in non-Hermitian Aubry-André-Harper models

Topological phases have recently witnessed rapid progress in non-Hermitian systems. Here we study a one-dimensional non-Hermitian Aubry-André-Harper (AAH) model with imaginary periodic or quasiperiodic modulations. We demonstrate that the non-Hermitian off-diagonal AAH models can host zero-energy mo...

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Bibliographic Details
Published in:Physical review. B 2020-01, Vol.101 (2), p.1, Article 020201
Main Authors: Zeng, Qi-Bo, Yang, Yan-Bin, Xu, Yong
Format: Article
Language:English
Subjects:
Circuits
Quasicrystals
Topology
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Summary:Topological phases have recently witnessed rapid progress in non-Hermitian systems. Here we study a one-dimensional non-Hermitian Aubry-André-Harper (AAH) model with imaginary periodic or quasiperiodic modulations. We demonstrate that the non-Hermitian off-diagonal AAH models can host zero-energy modes at the edges. In contrast to the Hermitian case, the zero-energy mode can be localized only at one edge. Such a topological phase corresponds to the existence of a quarter winding number defined by eigenenergy in momentum space. We further find the coexistence of a zero-energy mode located only at one edge and topological nonzero-energy edge modes characterized by a generalized Bott index. In the incommensurate case, a topological non-Hermitian quasicrystal is predicted where all bulk states and two topological edge states are localized at one edge. Such topological edge modes are protected by the generalized Bott index. Finally, we propose an experimental scheme to realize these non-Hermitian models in electric circuits. Our findings add another direction for exploring topological properties in Aubry-André-Harper models.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.101.020201