Topological edge modes and localization transition in quasiperiodic graphene multilayer arrays

•We study theoretically and numerically both commensurate and incommensurate AAH graphene lattices and realize the topological edge modes of SPPs and localization transition from extended to all-localized wavefunctions, respectively.•The graphene systems can enable flexible and efficient modulation for constructing AAH lattice, thus circumventing the drawbacks of limited modulation depths in all dielectric AAH waveguide systems.•The topological edge states and localization transitions for graphene SPPs may be utilized for developing plasmonics devices operating in deep subwavelength scale on fully flat and compact platforms.