Weyl points and Dirac lines protected by multiple screw rotations

Akira Furusaki

doi:10.1016/j.scib.2017.05.014

Abstract

In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron’s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 (P212121) and No. 198 (P213), which have three orthogonal screw rotation axes. In the case of space groups No. 61 (Pbca) and No. 205 (Pa-3) that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the Γ point and R point, respectively.

Highlights

Topological states of matter have attracted a lot of attention since the discovery of topological insulators.1,2 A focus of very active recent studies is topological semimetals3–5 that have gapless excitations in the bulk with linear energy dispersion (Weyl or Dirac fermions)
In this paper we study the band structure of materials whose crystalline symmetry is governed by nonsymmorphic space groups (SGs) 19, 61, 198, and 205, which have multiple screw rotation symmetries
Our study is motivated by recent experiments and first-principle calculations on cubic chiral materials NiSbS and PdBiSe (SG198)24 and CoSe2 (SG205),25 which revealed complex Fermi surface structures and band touchings that are characteristic of nonsymmorphic crystals with strong spin-orbit coupling

Summary

INTRODUCTION

Topological states of matter have attracted a lot of attention since the discovery of topological insulators. A focus of very active recent studies is topological semimetals that have gapless excitations in the bulk with linear energy dispersion (Weyl or Dirac fermions). It has been known that nonsymmorphic crystal symmetries, such as screw rotation and glide mirror, enforce energy bands to stick together at some high symmetry points when spin-orbit coupling is negligible. Our study is motivated by recent experiments and first-principle calculations on cubic chiral materials NiSbS and PdBiSe (SG198) and CoSe2 (SG205), which revealed complex Fermi surface structures and band touchings that are characteristic of nonsymmorphic crystals with strong spin-orbit coupling. We first discuss energy band structures of electron systems with strong spin-orbit coupling in crystals of SG19 and SG198. (A discussion on the band topology for the SG19 in the absence of spin-orbit coupling can be found in Ref.26.) Throughout this paper we assume that electron systems are invariant under time-reversal transformation Θ, which is an antiunitary operator satisfying Θ2 = −1.

Space group No 19

Space group No 198

SUMMARY