Electronic and magnetic properties of twisted graphene nanoribbon and M？bius strips: first-principles calculations

The geometrical, electronic, and magnetic properties of twisted zigzag-edged graphene nanoribbons (ZGNRs) and novel graphene M\"obius strips (GMS) are systematically investigated using first-principles density functional calculations. The structures of ZGNRs and GMS are optimized, and their stabilities are examined. The molecular energy levels and the spin polarized density of states are calculated. It is found that for twisted ZGNRs, the atomic bonding energy decreases quadratically with the increase of the twisted angle, and the HOMO-LUMO gap are varying in a sine-like behavior with the twisted angle. The calculated spin densities reveal that the ZGNRs and GMS have antiferromagnetic ground states, which persist during the twisting. The spin flips on the zigzag edges of GMS are observed at some positions.