  We consider asymmetric and symmetric dimerized two-leg ladders, comprising of
four different lattice points per unit cell, illuminated by circularly
polarized light. In the asymmetric dimerized ladder case, rungs are not
perpendicular to the ladder's legs whereas the rungs are perpendicular to the
legs for the symmetric one. Using the Floquet theory, we obtain an effective
Hamiltonian to study topological properties of the systems. Depending on the
dimerization strength and driving amplitude, it is shown that topologically
protected edge states manifest themselves not only as a zero-energy band within
the gap between conduction and valence band but also as finite-energy curved
bands inside the gap of subbands. The latter one can penetrate into bulk states
and hybridize with the bulk states revealing hybridized Floquet topological
metal phase with delocalized edge states in the asymmetric ladder case.
However, in the symmetric ladder, the finite-energy edge states while remaining
localized can coexist with the extended bulk states manifesting Floquet
topological metal phase.
