2021/12/31 by Andy Knoll, Carsten Timm
Materials Science · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Brillouin zone #Combinatorics #Degenerate energy levels #Geometry #Graphene research and applications #Homogeneous space #Mathematics #Physics #Point group #Point reflection #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.105.115109
25 pages, 12 figures
openalex publication_date 2022/03/07 · arxiv created 2022/03/21 · arxiv updated 2022/03/22 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/05
Symmetry-protected topological semimetals are at the focus of solid-state research due to their unconventional properties, for example, regarding transport. By investigating local two-band Bloch Hamiltonians in the spin-1/2 basis for the 122 magnetic point groups, we classify twofold-degenerate band touchings such as Weyl points, robust nodal lines on axes and in mirror planes, and fragile nodal lines. We find that all magnetic point groups that lack the product of inversion and time-reversal symmetries can give rise to topologically nontrivial band touchings. Hence, such nodes are the rule rather than the exception and, moreover, do not require any complicated multiband physics. Our classification is applicable to every momentum in the Brillouin zone by considering the corresponding little group and provides a powerful tool to identify magnetic and nonmagnetic topological semimetals.