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

Abstract

Node line (NL) band-touchings protected by mirror symmetry (named as m-NL), the product of inversion and time reversal symmetry S = PT (s-NL), or nonsymmorphic symmetry are nontrivial topological objects of topological semimetals (SMs) in the Brillouin Zone (BZ). In this work, we screened the family of MgSrSi-type crystals using first principles calculations, and discovered that more than 70 members are NLSMs. 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 multiloop structure of NLs were predicted in AsFeNa and PNiNb. Our work may shed light on search for exotic multi-loop NLSMs in real materials.

Topological carbon materials: A new perspective

“…In the nodal-line semimetals [184][185][186][187][188][189][190][191][192][193][194][195][196][197][198][199][200][201] , the band crossings form 1D lines in momentum space, instead of discrete points. Because lines can be deformed into many different shapes (e.g., a ring or a knot), there exist diverse topological phases for the nodal lines [202][203][204][205][206][207][208][209][210][211][212][213][214][215][216][217][218] , such as nodal chains, nodal links, and Hopf chains, etc. In the third type of TMs, the band crossings form a 2D surface 51,[219][220][221][222] , where each point is a crossing point whose dispersions are linear along the surface normal direction.…”

“…In 3D, two bands can cross each other along a closed curve or at a surface at discrete Dirac or Weyl points, as discussed above. When it is a curve, the curve is called a nodal line [270][271][272][273][274][275][276][277][278] , which may either take the form of an extended line running across the Brillouin zone (BZ), whose ends meet at the BZ boundary 184 , or wind into a closed loop inside the first BZ 276 , or even form a chain consisting of several connected loops (nodal chains) 217 . Topological semimetals with such line crossings are called topological nodal-line semimetal [279][280][281][282][283][284] .…”

Degenerate topological line surface phonons in quasi-1D double helix crystal SnIP

“…10 Among the degenerate points, twofold degenerate Weyl points always appear in pairs that can be topologically characterized with opposite Chern numbers, [11][12][13][14] and fourfold degenerate Dirac points have a linear dispersion in both electronic [15][16][17][18][19][20] and phononic systems. 21,22 When the band crossings are one-dimensional in momentum space, they can form nodal lines, nodal rings or nodal chains, depending on their shape, [23][24][25][26][27][28][29][30][31] and these line crossings are protected by symmetries such as mirror or PT (where P is the spatial inversion symmetry and T is the time reversal symmetry). 32,33 Recent advances, using both group theoretical analysis and high-throughput calculations, have enabled a comprehensive understanding of bulk band degeneracies in both electrons [34][35][36] and phonons.…”

Electronic structure of the Si-containing topological Dirac semimetal CaAl2Si2

“…Si, Ge, Al, Ca…). Recently, the search over the material database suggests a plethora of TQMs with non-trivial topological electronic structure, 27 including many Si-containing compounds such as BaSi 2 27 and TiNiSi 28 . Nevertheless, only few have been experimental confirmed, such as ZrSiS (topological Dirac nodal line semimetal) 29,30 and CoSi (chiral semimetal with multifold fermions) 31,32 .…”