Three-dimensional Kagome graphene networks and their topological properties

Kagome graphene is a single-layer carbon nanosheet possessing Kagome bands. Here, we propose two types of three-dimensional (3D) Kagome graphene networks (KGNs), which are formed by linking one-dimensional (1D) Kagome graphene nanoribbons. The carbon allotropes show good stabilities although they are completely made of triangle rings. Their cohesive energies are smaller than that of T-carbon approximate 0.3 eV/atom. Remarkably, the new structures exhibit interesting topological properties. The first type of KGN (KGN-1) inherits electronic properties of Kagome graphene. It has two sets of orbital-frustration-induced Kagome bands, and crossings between the bands lead to three kinds of nodal rings, i.e., type I, type II and a critical phase between them. These nodal rings can be observed successively by hole doping. The second type of KGN (KGN-2) is a topological metal. There exist a coexisting phase of a nodal surface and two nodal lines in the momentum space, which are originated from the quantum states in the 1D nanoribbons. In addition, two kinds of electron channels are found in KGN-2.