▎ 摘　　要

Low-energy electronic excitations in free-standing graphene (gr) and gr(2 x 2)/K interface have been studied based on ab initio band structure and linear-response theory. For pristine graphene, the calculated linear dispersion of collective interband transitions around the Dirac cone is in good agreement with experiments. At the gr/K interface, in addition to the doping-enhanced linear mode, a nonlinear plasmon develops with increasing momentum transfers along the Gamma K direction. Using a model-doped freestanding graphene, we revealed that the nonlinear mode originates from the anisotropic band dispersion at the Fermi level, and its collectivity emerges as the carrier density increases. These findings have implications for measurements of electronic excitations in metal-supported graphene sheet. (C) 2011 Elsevier Ltd. All rights reserved.