Observation of a saddle-loop van Hove singularity

Abstract Exploiting electronic singularities to drive emergent quantum phenomena is a key basis in condensed matter physics, yet this powerful strategy has been largely limited to two dimensions, leaving the potential of three-dimensional materials often inaccessible. A “saddle-loop” singularity—a one-dimensional ring of saddle points—has been proposed as a way to extend the concept of van Hove singularities to three-dimensional electron systems, but has remained experimentally elusive. Here, we provide the direct experimental evidence for the saddle‑loop singularity in Pt(Bi _{1− x} Se _x ) ₂ , using angle‑resolved photoemission spectroscopy. We also show that the saddle loop is positioned closer to the Fermi level at low x values where the superconducting critical temperature is higher. Furthermore, our advanced theoretical calculations reveal that the saddle loop originates from inter-orbital hybridization, establishing a generalizable design concept. Our findings demonstrate a viable mechanism for realizing singular electronic states in three-dimensional electron systems, providing a platform to investigate correlation-driven phenomena in three dimensions.