Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative curvature, called Mackay-Terrones crystals (MTC), have been proposed and experimentally explored, yet their topological properties remain to be discovered. Based on the first-principle calculations, we report an all-carbon MTC with topologically non-trivial electronic states by exhibiting node-lines in bulk. When the node-lines are projected on to surfaces to form circles, "drumhead" like flat surface bands nestled inside of the circles are formed. The bulk node-line can evolve into 3D Dirac point in the absence of inversion symmetry, which has shown its plausible existence in recent experiments.
@article{arxiv.1411.2175,
title = {Topological Node-Line Semimetal in Three Dimensional Graphene Networks},
author = {Hongming Weng and Yunye Liang and Qiunan Xu and Rui Yu and Zhong Fang and Xi Dai and Yoshiyuki Kawazoe},
journal= {arXiv preprint arXiv:1411.2175},
year = {2015}
}