Size dependent electronic and magnetic properties of ultra thin graphene nanoribbons

We present the results of systematic investigation into size dependent electronic and magnetic properties of ultra thin graphene nanoribbons (GNRs) of finite and infinite length using spin polarized density functional calculation. The rectangular GNRs with width up to 1.40 nm with finite (2.50 nm) and infinite length were investigated. The ultra thin GNRs are found less stable in comparison to larger GNRs with binding energy increasing with increase in the size. All GNRs have shown finite HOMO-LUMO gap which decreases oscillatory as a function of width. HOMO-LUMO gap in the Finite length armchair GNRs is in range of 0.01-0.36 eV, where as in infinite length GNR the energy gap is in the range of 0.30-1.41 eV. Zigzag GNRs have shown very small HOMO-LUMO gap in the range 50-80 meV. The zigzag GNR have shown opening of energy band gap. However, for N = 8 and 10 layers, GNRs with zigzag edges are found to be ferromagnetic. The edge C atom on zigzag edges contribute magnetic moment of 0.94 mu(B) per C atom with total magnetic moment remaining constant with increase in the width. The energy difference between ferromagnetic and anti-ferromagnetic state decreases sharply with the increase in GNR width suggesting iso-energetic behavior in larger GNRs. The results are consistent with the reported experimental results.