Electronic properties of graphene nano-flakes: Energy gap, permanent   dipole, termination effect and Raman spectroscopy
  The electronic properties of graphene nano-flakes (GNFs) with different edge passivation is investigated by using density functional theory. Passivation with F and H atoms are considered: C$_{N_c}$ X$_{N_x}$ (X=F or H). We studied GNFs with $10<N_c<56$ and limit ourselves to the lowest energy configurations. We found that: i) the energy difference $\Delta$ between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) decreases with $N_c$, ii) topological defects (pentagon and heptagon) break the symmetry of the GNFs and enhance the electric polarization, iii) the mutual interaction of bilayer GNFs can be understood by dipole-dipole interaction which were found sensitive to the relative orientation of the GNFs, iv) the permanent dipoles depend on the edge terminated atom, while the energy gap is independent of it, and v) the presence of heptagon and pentagon defects in the GNFs results in the largest difference between the energy of the spin-up and spin-down electrons which is larger for the H-passivated GNFs as compared to F-passivated GNFs. Our study shows clearly the effect of geometry, size, termination and bilayer on the electronic properties of small GNFs.This study reveals important features of graphene nano-flakes which can be detected using Raman spectroscopy. 
Sandeep Kumar Singh, M. Neek-Amal, and F.M. Peeters
cond-mat.mtrl-sci