Abstract
We classify the band degeneracies in three-dimensional crystals with screw symmetry and broken symmetry, where stands for spatial inversion and for time reversal. The generic degeneracies along symmetry lines are Weyl nodes: chiral contact points between pairs of bands. They can be single nodes with a chiral charge of magnitude or composite nodes with or 3, and the possible values only depend on the order of the axis, not on the pitch of the screw. Double Weyl nodes require or 6, and triple nodes require . In all cases, the bands split linearly along the axis, and for composite nodes the splitting is quadratic on the orthogonal plane. This is true for triple as well as double nodes, due to the presence in the effective two-band Hamiltonian of a nonchiral quadratic term that masks the chiral cubic dispersion. If symmetry is present and is broken, there may exist on some symmetry lines Weyl nodes pinned to -invariant momenta, which in some cases are unavoidable. In the absence of other symmetries, their classification depends on , and the type of symmetry. With spinless such -invariant Weyl nodes are always double nodes, while with spinful they can be single or triple nodes. -invariant triples nodes can occur not only on sixfold axes but also on threefold ones, and their in-plane band splitting is cubic, not quadratic as in the case of generic triple nodes. These rules are illustrated by means of first-principles calculations for hcp cobalt, a -broken, -invariant crystal with symmetry, and for trigonal tellurium and hexagonal , which are -invariant, -broken crystals with threefold and sixfold screw symmetry, respectively.
3 More- Received 1 April 2017
DOI:https://doi.org/10.1103/PhysRevB.96.045102
©2017 American Physical Society