Floquet high Chern insulators in periodically driven chirally stacked multilayer graphene

Chirally stacked N-layer graphene is a semimetal with ±p ^N band-touching at two nonequivalent corners in its Brillioun zone. We predict that an off-resonant circularly polarized light (CPL) drives chirally stacked N-layer graphene into a Floquet Chern insulators (FCIs), aka quantum anomalous Hall insulators, with tunable high Chern number C _F = ±N and large gaps. A topological phase transition between such a FCI and a valley Hall (VH) insulator with high valley Chern number C _v = ±N induced by a voltage gate can be engineered by the parameters of the CPL and voltage gate. We propose a topological domain wall between the FCI and VH phases, along which perfectly valley-polarized N-channel edge states propagate unidirectionally without backscattering.