Effective band structures of multilayer graphene quasicrystals

In this paper, the electronic properties of several multilayer graphene quasicrystals are studied by means of the tight-binding method. The multilayer graphene quasicrystals are stacked in AA, AB or their combined orders, and the quasi-periodicity is introduced by rotating at least one layer by 30 degree. The periodic approximants of several multilayer graphene quasicrystals are proposed, and their effective band structures are derived by unfolding the band structures of approximants. The 30 degree twisted interface separates the system into subsystems, and our results show that these subsystems are coupled by the interlayer interactions crossing the interface but will retain their own band structures at low-energies. The band structures of all the subsystems with the same orientation are combined at the corners of the Brillouin zone, and scattered into their mirror-symmetric points inside the Brillouin zone, with weak and anisotropic spectral functions. Such mirror symmetry and combination effects are robust even if an external electric field is applied. Our results suggest that the 30 degree twisted quasicrystal interface can be used to engineer the band structures of multilayer graphene or other layered two-dimensional materials.