Type-I and Type-II Saddle Points and a Topological Flat Band in a Bi-Pyrochlore Superconductor CsBi2

The divergence of the electron density of states (DOS) plays an important role in enhancing many-body interactions and inducing various quantum phases in low-dimensional systems. However, such unique electronic structures remain experimentally elusive in three-dimensional (3D) systems, particularly those with strong spin-orbit coupling (SOC). Using angle-resolved photoemission spectroscopy and first-principles calculations for a Laves-phase superconductor CsBi$_2$, which features a Bi-pyrochlore 3D network with strong SOC, we identify two characteristic electronic structures with a large DOS. One is a dispersionless topological flat band with p-orbital character, locally formed around the U-K line, which enhances DOS near the Fermi level. The other involves type-I and type-II saddle points connected by a flat band, which cooperatively produce an enhancement in the DOS. Our findings suggest a novel mechanism for achieving a DOS enhancement and lay a foundation for exploring exotic phenomena driven by the interplay of multiple singularities with a large DOS, nontrivial topology, and strong SOC in 3D pyrochlores.