石墨烯- $N$单层膜及其多层膜的电子性质：奇偶效应和拓扑节线半金属相
Electronic properties of graphyne-$N$ monolayer and its multilayer: even-odd effect and topological nodal line semimetalic phases
摘要：
本文研究了石墨炔- $N$（由$sp$和$sp_2$键组成的平面碳片）的单层和ABC叠层的电子结构和拓扑性质。利用密度泛函理论和有效连续介质模型，我们发现苯环间碳-碳三键数$N$对能带结构的依赖性存在显著的奇偶效应.具体地说，偶- $N$石墨炔单层在费米能级附近具有双简并导带和价带，并且在其ABC多层中，双简并带的带反转导致具有非平凡$\mathbb{Z}_2$电荷的半金属相。相反，奇$N$单层在单独的谷中具有单简并带，并且其ABC多层可以仅具有$\mathbb{Z}_2$ -平凡节线。具有较大$N$的ABC石墨烯由于较小的层间耦合而倾向于平凡绝缘体，而外部压力诱导从平凡相到节线半金属相的拓扑相变。
英文摘要：
We study the electronic structure and topological properties of monolayer and ABC-stacked multilayer of graphyne-$N$, which are a family of planar carbon sheets consisting of $sp$ and $sp_2$-bonding. By using the density-functional theory and the effective continuum model, we find a striking even-odd effect in the dependence of the band structure on $N$ (the number of carbon-carbon triple bonds between neighboring benzene rings). Specifically, even-$N$ graphyne monolayer has doubly-degenerate conduction and valence bands near the Fermi energy, and in its ABC multilayer, the band inversion of the doubly-degenerate bands leads to a nodal-line semimetal phase with non-trivial $\mathbb{Z}_2$ monopole charge. In contrast, odd-$N$ monolayer has singly-degenerate bands in separate valleys, and its ABC multilayer can have only $\mathbb{Z}_2$-trivial nodal lines. ABC graphynes with larger $N$ tend to be trivial insulators because of smaller interlayer coupling, while the external pressure induces a topological phase transition from the trivial phase to the nodal line semimetal phase.
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