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In the frame work of density functional theoretical calculations, the electronic and lattice dynamical properties of graphene (multilayers and supercell) have been systematically investigated and analyzed using the plane wave pseudopotentials within the generalized gradient approximation and local density approximation functional. We have also studied the functionalization of graphene by adsorption and absorption of transition metals like Al and Ag. We find that the electronic properties exhibit large sensitivity to the number of layers and doping. The Al and Ag doped graphene exhibits peak at Fermi level in the density of states arising from the flat bands near Fermi level. The bonding of metal atoms and graphene leads to a charge transfer between them and consequently shift Fermi level with respect to the conical point at K-point. The adsorption of Ag/Al atoms suggests an effective interaction between the adatoms and graphene layers without disturbing the original graphene structure of lower graphene layers. Compared to single layer graphene, the optical phonon E2g mode and out of plane ZA mode at Γ-point splits in the bi-, tri- and four- layer graphene. We observe a shift for highest optical branch at Dirac K- point. We find that the different derivatives of graphene have different phonon dispersion relations. We demonstrate that there is removal of degeneracy of ZO/ZA modes at K- point with transition metal doping. The highest optical phonon branch becomes flat at Dirac point with doping of transition metals. Our study points that the substituted graphene sheets can have potential applications in ordered-disordered separated quantum films with two to four layers of atoms and new nano devices using graphene.


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