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

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

doi:10.1038/s41524-018-0147-y

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.

Highlights

Depending on the dimensionality of band crossings, topological semimetals are classified into three categories, the Weyl semimetals (WSMs)[3,4,5,6,7,8] or Dirac semimetals (DSMs),[9,10,11] node-line semimetals (NLSMs),[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] and node-surface semimetals (NSSMs).[42,43]
In this work, using first principles calculations, we screened the family of MgSrSi-type crystals which consists of 660 members, and found more than 70 compounds are NLSMs showing a variety of NL structures
In contrast to a previous report in which the member AsRhTi was predicted to be a NLSM with a single NL band crossing,[22] we found in this material a new type of multiloop NL structure as shown in Fig. 1d, where a s-NL sticks to a mNL at some “nexus point” and penetrates the invariant plane of m-NL at some general point (denoted by E in Fig. (1d))

Summary

Introduction

The band crossings of the conduction and valence bands in a topological semimetal are interesting topological objects of Brillouin Zone (BZ) which bring about unique electronic structures and electrical properties, such as giant magnetoresistance, parity anomaly and “drum-head” states at material’s surfaces.[1,2] Depending on the dimensionality of band crossings, topological semimetals are classified into three categories, the Weyl semimetals (WSMs)[3,4,5,6,7,8] or Dirac semimetals (DSMs),[9,10,11] node-line semimetals (NLSMs),[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] and node-surface semimetals (NSSMs).[42,43] Unlike the DSMs and WSMs whose band crossings take place at discrete points in the BZ, the band crossings of NLSMs form closed loops. In this work, using first principles calculations, we screened the family of MgSrSi-type crystals which consists of 660 members, and found more than 70 compounds are NLSMs showing a variety of NL structures.

Results

Conclusion