Trans-dimensionality of electron/hole channels in multilayer in-plane heterostructures comprising graphene and hBN superlattice

Using density functional theory, we investigated trilayer in-plane heterostructures consisting of graphene and hBN strips in terms of their interlayer stacking arrangements. The trilayer hBN/graphene superlattices possess flat dispersion bands at their band edges, the wave function distribution of which strongly depends on the interlayer stacking arrangement. The wave functions of the valence and conduction band edges of the trilayer heterostructure with AA' stacking are distributed throughout the layers implying a two-dimensional carrier distribution. In contrast, we found one-dimensional carrier channels along the border between graphene and hBN for electrons and holes in the trilayer heterosheet with rhombohedral interlayer stacking. These unique carrier distributions are ascribed to the interlayer dipole moment arising from asymmetric arrangements of B and N atoms across the layers. Therefore, the trilayer in-plane heterostructures of graphene and hBN superlattice possess trans-dimensional carriers in terms of their interlayer stacking arrangement.