▎ 摘　　要

We study the geometries, energetics, and electronic structures of free-standing graphene with long range structural undulations. Our calculations, which are based on density functional theory, show that the energy cost to induce the structural corrugation is about a few tens of meV per C atom which is similar to the total energy of the C atoms in carbon nanotubes. Our tight-binding molecular dynamics simulations confirmed that graphene exhibits long-range structural undulation at temperatures above 400 K. Moreover, our detailed analysis of the electronic energy band near the Fermi level shows that the linear dispersion band is sensitive to these structural undulations, which leads to semiconducting properties with an energy gap of a few meV. (C) 2012 The Japan Society of Applied Physics