Complex intrinsic surface states of pyrite ferromagnetic topological semimetal CoS₂

The ferromagnet CoS₂, a typical pyrite structure, was recently discovered to have multi-nodal structures. In this work, we observe many complex intrinsic surface states in CoS₂ and find the different origins of these various surface states. We find that CoS₂ not only exhibits a variety of topological nodal structures but also has an obstructed-atomic-limit feature. Thus, Fermi arc, drumhead, and obstructed atomic-center-induced surface states (OASs) are accessible in this system. Interestingly, OASs exhibit a clear Dirac-like crossing sitting at Fermi level protected by glide mirror symmetry and some surface states spreading the whole Brillouin zone. Furthermore, combining first-principle calculation and experimental results, we observe that some additional spin-polarized surface states cannot be explained by the multi-nodal structures and OASs. These unique surface states spreading throughout the whole Brillouin zone are dubbed crystal field-enforced surface states (CFSs), i.e., this is because the S octahedron surrounding each Co is broken at the surface. In addition, we find that due to the bulk nature of the CoS₂ crystal structure, at least one of the OASs and CFSs always appears regardless of the choice of surface termination. These diverse origins of intrinsic surface states are beneficial to plenty of potential applications and explain the novel physical properties recently discovered in experiments, such as high-performance electrocatalytic activity.