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.

拓扑半金属是一类引人入胜的量子材料，具有非凡的电子和传输特性。近年来，这些材料因其基本意义和潜在的器件应用而引起了极大的兴趣。大量研究表明，三维石墨烯网络支持具有两种连续节线的拓扑半金属：一种是在布里渊区形成闭合的节环，另一种是遍历整个布里渊区以进行周期性连接。碳具有可忽略的自旋轨道耦合，非磁性和同素异形体的多样性，这使其在实现拓扑结线半金属方面非常有前途。在这里，我们回顾了提出各种碳同素异形体以实现这两种类型的节点线半金属的最新努力。节点环或线受时间反转和空间反转对称性的共存保护。将这些结线或环投影到特定表面时，会出现鼓面状的表面平坦带。基于这些平坦带，电子-电子相关效应将诱发陈绝缘子和高温超导体。Mott绝缘体和超导体在与平面带相关的双分子层石墨烯中的最新发现，使得这些经过审查的工作非常重要和有意义。陈恩绝缘体和高温超导体将受到电子-电子相关效应的感应。Mott绝缘体和超导体在与平面带相关的双分子层石墨烯中的最新发现，使得这些经过审查的工作非常重要和有意义。陈恩绝缘体和高温超导体将受到电子-电子相关效应的感应。Mott绝缘体和超导体在与平面带相关的双分子层石墨烯中的最新发现，使得这些经过审查的工作非常重要和有意义。