Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

Abstract

A non-Hermitian generalization of the Su-Schrieffer-Heeger model driven by a periodic external potential is investigated, and its topological features are explored. We find that the bi-orthonormal geometric phase acts as a topological index, well capturing the presence/absence of the zero modes. The model is observed to display trivial and non-trivial insulator phases and a topologically non-trivial M$\ddot{o}$bius metallic phase. The driving field amplitude is shown to be a control parameter causing topological phase transitions in this model. While the system displays zero modes in the metallic phase apart from the non-trivial insulator phase, the metallic zero modes are not robust, as the ones found in the insulating phase. We further find that zero modes' energy converges slowly to zero as a function of the number of dimers in the M$\ddot{o}$bius metallic phase compared to the non-trivial insulating phase.

arXiv comment13 pages, 8 figures. An error in implementing PBC in Figs. 7,8 of the previous version is rectified, and the related discussion is updated

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