Floquet High Chern Insulators in Periodically Driven Chirally Stacked Multilayer Graphene

Chirally stacked N-layer graphene is a semimetal with p$^{\mathrm{N}}$ band-touching at two nonequivalent corners in its Brillioun zone. We predict that a off-resonant circularly polarized light (CPL) drives chirally stacked N-layer graphene into a Floquet Chern Insulators (FCIs), a.k.a. quantum anomalous Hall insulators, with tunable high Chern number C$_{\mathrm{F}}=+$/-N and large gaps. A topological phase transition between such a FCI and a valley Hall (VH) insulator with high valley Chern number C$_{\mathrm{v}}=+$/-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.