Topological Floquet Flat Bands in Irradiated Alternating Twist Multilayer Graphene

We study the appearance of topological Floquet flat bands in alternating-twist multilayer graphene, which has alternating relative twist angle $\pm\theta$ near the first magic angle. While the system hosts both flat bands and a steep Dirac cone in the static case, the circularly polarized laser beam can open a gap at the Moir\'{e} $K$ point and create Floquet flat bands carrying nonzero Chern numbers. Considering recent lattice-relaxation results, we find that the topological flat band is well-isolated for the effective interlayer tunneling in $n=3, 4, 5$ layers. Such dynamically produced topological flat bands are potentially observed in the experiment and thus provide a feasible way to realize the fractional Chern insulator.