▎ 摘　　要

Graphene ripples possess peculiar essential properties owing to the strong chemical bonds, as an investigation using first principle calculations clearly revealed. Various charge distributions, bond lengths, energy bands, and densities of states strongly depend on the corrugation structures, ripple curvatures and periods. Armchair ripples belonging to a zero-gap semiconductor display split middle-energy states, while the zigzag ripples exhibit highly anisotropic energy bands, semi-metallic behavior implicated by the destruction of the Dirac cone, and the newly created critical points. Their density of states exhibit many low-lying prominent peaks and can explain the experimental measurements. There exist certain important similarities and differences between graphene ripples and carbon nanotubes. (C) 2014 Elsevier Ltd. All rights reserved.