Floquet topological transitions in a driven one-dimensional topological insulator

The Su--Schrieffer--Heeger model of polyacetylene is a paradigmatic Hamiltonian exhibiting nontrivial edge states. By using Floquet theory we study how the spectrum of this one-dimensional topological insulator is affected by a time-dependent potential. In particular, we provide evidence of the competition among different photon-assisted processes and the native topology of the unperturbed Hamiltonian to settle the resulting topology at different driving frequencies. While some regions of the quasienergy spectrum develop new gaps hosting Floquet edge states, the native gap can be dramatically reduced and the original edge states may be destroyed or replaced by new Floquet edge states. Our study is complemented by an analysis of the Zak phase applied to the Floquet bands. Besides serving as a simple example for understanding the physics of driven topological phases, our results could find a promising testing ground in cold-matter experiments.