Topological Node-Line Semimetal in Three Dimensional Graphene Networks
  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. 
Hongming Weng, Yunye Liang, Qiunan Xu, Rui Yu, Zhong Fang, Xi Dai and   Yoshiyuki Kawazoe
cond-mat.mes-hall cond-mat.mtrl-sci