Fig. 1: Symmetries, band topology, Fermi surface protectorates and band structure of ferromagnetic MnSi.
From: Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
a, Action of the magnetic screw rotations and time-reversal symmetry (TRS) on the k-points in the BZ. b, Pairs of energy bands E(k) close to the Fermi energy EF forming a topological NP (red line) on the BZ boundary that is perpendicular to the screw-rotation axis. This NP is the topological partner of a single Weyl point (WP) in the bulk (blue dot) of opposite topological charge. c, High-symmetry paths in the cubic primitive BZ. Special k-points are denoted by the orthorhombic primitive notation with subscripts for easier identification. d, Generic tight-binding band structure illustrating the generic band degeneracies of ferromagnetic MnSi with its magnetic space group, SG 19.27, namely Weyl points, four-fold degenerate points (FPs), NPs and TPs. e, Band structure of ferromagnetic MnSi for magnetization along [010] as calculated using DFT. Ten bands cross the Fermi level, as distinguished by different colours corresponding to the FS sheets numbered in f. f, Calculated FS sheets adapted to match the experimental data under magnetic field along [010], as discussed in Methods. Note the presence of NPs on the BZ boundaries, kx = ±π and kz = ±π, as well as TPs marked in red. a.u., arbitrary units.
