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

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 nontrivial insulator phases and a topologically nontrivial Möbius 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 nontrivial insulator phase, the metallic zero modes are not robust, as are 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 Möbius metallic phase compared to the nontrivial insulating phase.