  We report on the theoretical investigation of the topological properties of a
periodically quenched one-dimensional dimerized lattice where a piece-wise
constant Hamiltonian switches from $h_1$ to $h_2$ at a partition time $t_p$
within each driving period $T$. We examine different dimerization patterns for
$h_1$ and $h_2$ 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 quasi-energy 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.

Mesoscale and Nanoscale Physics