▎ 摘　　要

The energy gap of extended states in zigzag graphene nanoribbons (ZGNRs) was examined on the basis of density-functional theory. In isolated ZGNRs, the energy gap is inversely proportional to the width of ribbon. It agrees well with the results from the Dirac equation in spin-unpolarized ZGNRs, although the considered ZGNRs have spin-polarized edges. However, the energy gap in SiC-doped ZGNRs cannot be modeled by effective width approximation. The doping also lifts the spin-degenerate of edge states and results in a metallic-like band structure near the Fermi level in SiC-doped ZGNRs. Our calculations may be helpful for understanding the origin of the reported single-channel ballistic transport in epitaxial graphene nanoribbons. (C) 2016 Elsevier B.V. All rights reserved.