Relation between the Stacking Shift and Electronic Structure in Layered Materials: General Theory

Atomically thin materials such as graphene, transition-metal dichalcogenide and phosphorene form various stacking polytypes and their electronic properties are sensitively dependent on the stacking pattern. Although there have been a variety of theoretical and experimental studies on such stacking-dependent properties, a general theory bridging individual materials has been lacking. Recently, we have found that the excitons in multilayered MoS₂ can be protected from the interlayer hopping process when the system adopts a specific 3R stacking [RA et al., PRAppl. 4, 014002]. This protection is induced by an interference of the plane-wave part of the Bloch function. On top of this finding, we study such interference effect in general layered structures. We prove that the interference prohibits the interlayer hopping for the Bloch states at specific points in the Brillouin zone. The positions of such points respect only the interlayer shift and are applicable to any materials. We demonstrate by the first-principles calculations that this effect dominates the stacking dependence of the electronic band structure in graphene, boron nitride, transition metal dichalcogenide and phosphorene [RA et al., PRB 95, 245401].