Using first principles pseudopotential density functional theory calculations, we find that terminating zigzag graphene nanoribbons (ZGNR) with monovalent alkali atoms at a reduced concentration has a dramatic impact on their properties. In particular, using sodium atoms for the saturation of ZGNR edges at half the concentration of edge-carbon atoms make it a one dimensional, perfect semimetal, where the valance and conduction bands meet at only a single, Dirac-like point. Unlike pristine graphene, the Dirac-"cones" of Na-ZGNR is not symmetric with respect to wave vector, but rather it is tilted.
@article{arxiv.1105.0547,
title = {Sodium-terminated zigzag graphene nanoribbon: A one-dimensional semimetal with a tilted Dirac cone},
author = {Ozan Arı and İbrahim Dursun and R. Tuğrul Senger},
journal= {arXiv preprint arXiv:1105.0547},
year = {2016}
}