Edge-State-Induced Stacking of Zigzag Graphene Nanoribbons

We have investigated the structural stabilities and electronic properties for AA and the Bernal-stacked AB bilayer zigzag graphene nanoribbons (ZZGNRs) using first-principles calculations within density functional theory. The AB-stacked ZZGNR exhibits the spin-polarized state, while the AA-stacked ZZGNR has the nonmagnetic ground state, being more energetically stable than the AB-stacked one. For the AA-stacked ZZGNR, the interaction between the so-called edge states rather than the van der Waals (vdW) interaction plays an important role: the occupied up-spin and the unoccupied down-spin states at one end of ZZGNR interact with each other, and vice versa at the other end, forming the non-spin-polarized bonding and antibonding states at the zigzag edge. Thus, the structural stability for the AA-stacked ZZGNR is dominated by the trade-off between the edge-edge interaction and the vdW interaction of the basal plane of GNRs.