Topological node-line semimetal in three-dimensional graphene networks

TLDR

Graphene’s remarkable properties arise from its Dirac‑point electronic structure, and while three‑dimensional graphene networks (Mackay‑Terrones crystals) have been proposed and experimentally explored, their topological characteristics remain unknown. This study reports an all‑carbon Mackay‑Terrones crystal that hosts topologically non‑trivial electronic states manifested as bulk node‑lines. First‑principle calculations show that projecting these bulk node‑lines onto surfaces generates circular drumhead‑like flat bands inside the projected circles. The bulk node‑line can evolve into a three‑dimensional Dirac point when inversion symmetry is absent, a transition that recent experiments plausibly support.

Abstract

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.