Topological nodal line semimetals in graphene network structures

Topological semimetals are a fascinating class of quantum materials that possess extraordinary electronic and transport properties. These materials have attracted great interests in recent years for their fundamental significance and potential device applications. There have been intensive studies suggested that three-dimensional graphene networks support topological semimetals with two types of continuous nodal lines: one is to form closed nodal rings in Brillouin zone and the other ones traversing the whole Brillouin zone to be periodically connected. Carbon has negligible spin-orbit coupling, non-magnetism and great diversity of allotropes, which makes it very promising in realizing topological nodal line semimetals. Here we review recent efforts in proposing various carbon allotropes to realize these two types of nodal line semimetals. The nodal rings or lines are protected by the coexistence of time reversal and spatial inversion symmetries. When projecting these nodal lines or rings onto the certain surface, drumhead like surface flat bands will appear. Based on these flat bands, Chern insulator and high-temperature superconductor will be induced by electron-electron correlation effects. The recent discoveries of Mott insulator and superconductor in twisted bilayer graphene-related with flat bands have made these reviewed efforts very important and meaningful. [GRAPHICS]