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

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.

Node line semimetal states in tungsten-based materials

Node line semimetals(NLSMs) were characterized by one-dimensional band crossings in their bulk electronic structures.The nontrivial band topology of NLSM gives rise to "drumhead" surface electronic excitations that exhibits exotic physical properties.The symmetries of crystalline provide the needed protection of node line from being gapped out by the perturbations that preserve the symmetry.The progress of NLSM in tungsten-based materials is reviewed with an emphasis on their symmetry-based protection,characteristic electronic band structures and their response to the spin-orbit coupling(SOC)and breaking of time-reversal symmetry.The potential exploration directions of tungsten-based NLSM in the future are also discussed.