Floquet topological phase transitions in a periodically quenched dimer

We report on the theoretical investigation of the topological properties of a periodically quenched one-dimensional dimerized lattice where a piecewise constant Hamiltonian switches from h₁ to h₂ at a partition time t₏ within each driving period T. We examine different dimerization patterns for h₁ and h₂ and the interplay with the driving parameters that lead to the emergence of topological states both at zero energy and at the edge of the Brillouin-Floquet quasienergy zone. We illustrate different phenomena, including the occurrence of both edge states in a semimetal spectrum, the topological transitions, and the generation of zero-energy topological states from trivial snapshots. The role of the different symmetries in our results is also discussed.