npj Computational Materials

Multi-loop node line states in ternary MgSrSi-type crystals （三元MgSrSi型晶体中的多环节点线状态）
Jinling Lian, Lixian Yu, Qi-Feng Liang, Jian Zhou, Rui Yu & Hongming Weng
npj Computational Materials 5:10 (2019)
doi:s41524-019-0150-y
Published online:21 February 2019
Abstract| Full Text | PDF OPEN

摘要:受镜像对称（mirror symmetry, m-NLs）、空间反演和时间反演对称的乘积S = PT（s-NLs），或非简单空间群对称等保护的节点线能带交叉是拓扑半金属在布里渊区中的非平凡拓扑对象。本研究使用第一原理计算筛选了一系列的MgSrSi型三元晶体，并发现超过70个成员是节点线半金属。特别是在AsRhTi晶体中发现了一种新颖的多节线结构，其中一个s-NL在某个“链接点”处与一个m-NL稳健地接触，同时该s-NL还与另一个m-NL嵌套形成Hopf环链。与先前提出的由两个s-NL或两个m-NL形成的Hopf环链不同，由一个s-NL和一个m-NL形成的Hopf环链需要最小的三带模型来表征其基本电子结构。本研究还获得了AsRhTi晶体的不同表面上的相关拓扑表面态。在AsFeNb和PNiNb中预测了更复杂和奇特的NLs多环结构。我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。　　

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.

Editorial Summary

Multi-loop node line state: in ternary MgSrSi-type crystal（三元MgSrSi型晶体:多环节点线态）

该研究发现了70多种MgSrSi型晶体化合物在其带结构中存在节点线能带交叉。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。其中节点线（node-line, NL）半金属的带交叉形成闭环，但这仅是依据一些材料提出的概念，在实际材料中的直接证据则几乎没有。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，AsRhTi表现出新颖的多环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，同时该s-NL还与另一个m-NL嵌套形成一个Hopf-环链。这个Hopf-环链需要最小的三带k p模型来表征其基本电子结构。研究结果进一步展示了由非平凡NL结构所导致的拓扑表面态。拓扑表面态具有非平凡NL结构。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。

More than 70 kinds of MgSrSi-type crystals are node-line semimetals showing a variety of NL structures. The intersection of the conduction band and the valence band in the topological semimetal is an interesting topological object of the Brillouin zone, which endows unique electronic structure and electrical properties to the topological semimetal. Among them, the node-line (NL) semimetal band form a closed loop, but this is only a proposed concept based on some materials, and there is almost no direct evidence in real materials. A joint team led by Professor Qi-feng Liang from Shaoxing University and Professor Rui Yu from Wuhan University used the first principle calculation to screen the ternary crystal family of MgSrSi-type crystals which consists of 660 members, and discovered that more than 70 compounds were 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. This Hopf-link requires a minimal three-band k p model to characterize its basic electronic structure. Their study further demonstrates that these non-trivial NL structures induce topological surface states on the crystal surfaces. Their research may help find exotic multi-loop node-line semimetals in real materials.