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We consider asymmetric and symmetric dimerized two-leg ladders, comprising offour different lattice points per unit cell, illuminated by circularlypolarized light. In the asymmetric dimerized ladder case, rungs are notperpendicular to the ladder's legs whereas the rungs are perpendicular to thelegs for the symmetric one. Using the Floquet theory, we obtain an effectiveHamiltonian to study topological properties of the systems. Depending on thedimerization strength and driving amplitude, it is shown that topologicallyprotected edge states manifest themselves not only as a zero-energy band withinthe gap between conduction and valence band but also as finite-energy curvedbands inside the gap of subbands. The latter one can penetrate into bulk statesand hybridize with the bulk states revealing hybridized Floquet topologicalmetal phase with delocalized edge states in the asymmetric ladder case.However, in the symmetric ladder, the finite-energy edge states while remaininglocalized can coexist with the extended bulk states manifesting Floquettopological metal phase.

Floquet engineering of topological metal states and hybridization of edge states with bulk states in dimerized two-leg ladders