Network of topological nodal planes, multifold degeneracies, and Weyl points in CoSi

TL;DR

This paper uncovers a network of topological features in CoSi, including nodal planes, multifold degeneracies, and Weyl points, through combined experimental and theoretical analysis of its electronic structure.

Contribution

It identifies symmetry-enforced nodal planes and their role in the topological band crossing network in CoSi, filling gaps in understanding of its topological charges.

Findings

Observation of four Fermi surface sheets at R point

Evidence of symmetry-enforced orthogonality of wave functions

Presence of six- and fourfold degenerate crossings at R and Γ

Abstract

We report the identification of symmetry-enforced nodal planes (NPs) in CoSi providing the missing topological charges in an entire network of band-crossings comprising in addition multifold degeneracies and Weyl points, such that the fermion doubling theorem is satisfied. In our study we have combined measurements of Shubnikov-de Haas (SdH) oscillations in CoSi with material-specific calculations of the electronic structure and Berry curvature, as well as a general analysis of the band topology of space group (SG) 198. The observation of two nearly dispersionless SdH 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 NPs. Hence, irrespective of the spin-orbit coupling strength, SG198 features always six- and fourfold degenerate crossings at R and $\Gamma$ that are intimately connected to the topological charges distributed across the network.