npj: 多环节点线态—隐于三元晶体中的庐山面目

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拓扑半金属中导带和价带的带交叉是布里渊区的有趣拓扑对象，它赋予拓扑半金属独特的电子结构和电学性质。由镜像对称（mirror symmetry, m-NLs）、反转和时间反转对称S = PT（s-NLs）的乘积，或非对称性对称等保护的节点线带-接触，是布里渊区拓扑半金属的非平凡拓扑对象。拓扑半金属中的节点线（node-line, NL）半金属的带交叉形成闭环，尽管这一概念已依据多种材料提出过，但在实际材料中的直接证据几乎没有，因而，在凝聚态物理领域寻找具有干净和拓扑稳定的NL能带穿越费米能级的新材料仍然是一项艰巨的任务。

来自绍兴文理学院的梁奇锋教授和武汉大学的余睿教授领导的联合团队，使用第一原理计算，对MgSrSi型三元晶体族的660种晶体作了筛选，发现有70多种化合物是节点线半金属。由于空间群中反射对称性和时间反演对称性的共存，使得AsRhTi的带结构中包含有一种新颖的多环NL结构，其中由PT对称性保护的s-NL与由镜像对称保护的m-NL在一些“链接点”稳健地接触，同时s-NL与第二个m-NL交叉形成一个Hopf-环链。这个Hopf-环链需要最小的三带k p模型以有效描述费米表面上的低能电子及基本电子结构。同时研究结果也展示了由非平凡NL结构所导致的拓扑表面态。在AsFeNb和PNiNb亚组中发现了更奇特的多环NL结构。所有发现的节点线半金属都与Zintl的8-N价数规则一致，表明价数规则应该是搜索拓扑半金属的有用指标。他们的研究可能有助于在真实材料中寻找奇异的多环节点线半金属。

该文近期发表于npj Computational Materials 5: 10 (2019)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。

Multi-loop node line states in ternary MgSrSi-type crystals 

Jinling Lian, Lixian Yu, Qi-Feng Liang, Jian Zhou, Rui Yu & Hongming Weng 

Abstract Node line band-touchings protected by mirror symmetry (named as m-NLs), the product of inversion and time reversal symmetry S = PT (named as s-NLs), or nonsymmorphic symmetry are nontrivial topological objects of topological semimetals in the Brillouin Zone. In this work, we screened a family of MgSrSi-type crystals using first principles calculations, and discovered that more than 70 members are node-line semimetals. A new type of multi-loop structure was found in AsRhTi that a s-NL touches robustly with a m-NL at some “nexus point”, and in the meanwhile a second m-NL crosses with the s-NL to form a Hopf-link. Unlike the previously proposed Hopf-link formed by two s-NLs or two m-NLs, a Hopf-link formed by a s-NL and a m-NL requires a minimal three-band model to characterize its essential electronic structure. The associated topological surface states on different surfaces of AsRhTi crystal were also obtained. Even more complicated and exotic multi-loop structure of NLs were predicted in AsFeNb and PNiNb. Our work may shed light on search for exotic multi-loop node-line semimetals in real materials.

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