Network of Topological Nodal Planes, Multifold Degeneracies, and Weyl Points in CoSi

We showcase the importance of global band topology in a study of the Weyl semimetal CoSi as a representative of chiral space group (SG) 198. We identify a network of band crossings comprising topological nodal planes, multifold degeneracies, and Weyl points consistent with the fermion doubling theorem. To confirm these findings, we combined the general analysis of the band topology of SG 198 with Shubnikov-de Haas oscillations and material-specific calculations of the electronic structure and Berry curvature. The observation of two nearly dispersionless Shubnikov-de Haas frequency branches provides unambiguous evidence of four Fermi surface sheets at the R point that reflect the symmetry-enforced orthogonality of the underlying wave functions at the intersections with the nodal planes. Hence, irrespective of the spin-orbit coupling strength, SG 198 features always six- and fourfold degenerate crossings at R and Γ that are intimately connected to the topological charges distributed across the network.