Network of topological nodal planes and point degeneracies in CoSi

We report the experimental identification of symmetry-enforced topological nodal planes in CoSi which together with multifold point degeneracies and Weyl points form a network of band crossings in total satisfying the Nielsen-Ninomiya no-go theorem. For this, we have combined measurements of Shubnikov-de Haas oscillations in CoSi with material-specific electronic structure calculations and a symmetry analysis of space group 198, in which CoSi crystallizes [1]. The observation of two nearly dispersionless Shubnikov-de Haas frequency branches is shown to provide clear evidence of four distinct Fermi surface sheets around the R point of the Brillouin zone (BZ) and of the symmetry-enforced orthogonality of the wave functions at the intersections with the nodal planes [2]. These results in combination with our symmetry analysis let us infer that the sum of topological charges of band crossings in the interior of the BZ is forced to be odd and therefore needs to be compensated by a topological charge of the nodal planes on the BZ boundary, as predicted in [3]. Therefore, a comprehensive analysis of all charges in the network needs to go beyond point degeneracies and take the topological nodal planes into account.

[1] Huber et al., arXiv:2107.02820 (2021)

[2] Wilde et al., Nature 594, 374 (2021)

[3] Yu et al., Phys. Rev. B 100, 041118 (2019)