Magic angles and flat Chern bands in alternating-twist multilayer graphene system

Abstract

Based on the effective continuum model, we study alternating-twist multilayer graphene system and emergence of magic angles and flat band topology. All the alternating-twist multilayer graphene system (from triple layers to few layers) are found to have flat bands at magic angles where the area of AA stacking equals n-fold (n is an integer) electron cyclotron area. From the pseudo-Landau-level representation, there is always an isolated Dirac band in the alternating-twist graphene system constructed by odd number of layers. Since each pair of flat bands can be perceived as the zeroth pseudo-Landau-levels in two dimensional Dirac fermions, electron in the flat band pair can feel a pseudo-magnetic field with the same magnitude but the opposite sign. Calculated Chern number for each flat band is +1 (or -1) which can be tuned by twisting in the vicinity of magic angles or by gating. The concurrent appearance of strong correlation and band topology of flat bands in the alternating-twist multilayer graphene may pave an avenue for the new understanding of superconductivity observed in triple-layered graphene, and supply a new playground for realizing (quantum) anomalous Hall effect.