Topological semimetals are characterized by the nodal points in their electronic structure near the Fermi level, either discrete or forming a continuous line or ring, which are responsible for exotic properties related to the topology of bulk bands. Here we identify by ab initio calculations a distinct topological semimetal that exhibits nodal nets comprising multiple interconnected nodal lines in bulk and have two coupled drumheadlike flat bands around the Fermi level on its surface. This nodal net semimetal state is proposed to be realized in a graphene network structure that can be constructed by inserting a benzene ring into each $\text{C}─\text{C}$ bond in the bct-${\mathrm{C}}_4$ lattice or by a crystalline modification of the (5,5) carbon nanotube. These results expand the realm of nodal manifolds in topological semimetals, offering a new platform for exploring novel physics in these fascinating materials.

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石墨烯网络结构中的拓扑节点网半金属

拓扑半金属的特征是其电子结构中的费米能级附近的节点（离散的或形成连续的线或环），这些节点负责与体带拓扑有关的奇异特性。在这里，我们通过从头算来确定一种独特的拓扑半金属，该半金属呈现出包含多个相互连接的散装节点线的节点网，并且在其表面上围绕费米能级具有两个耦合的鼓面状扁平带。提出该节点净半金属态可以在石墨烯网络结构中实现，该结构可以通过将苯环插入每个$\text{C}─\text{C}$ 结合在bct中${\mathrm{C}}_4$晶格或通过（5,5）碳纳米管的结晶修饰而获得。这些结果扩展了拓扑半金属中节点流形的范围，为探索这些引人入胜的材料中的新物理提供了新的平台。