General Theory of Vortex Topology in Conventional Superconductors

We develop a systematic theoretical framework for diagnosing emergent topological physics of vortex-bound states in s-wave spin-singlet superconductors. Our central result is that vortex topology is intrinsically dictated by real-space invariants of the normal-state electronic bands, which characterize the topological spectral flow under adiabatic flux insertion. This framework enables direct prediction of vortex topological properties from the symmetry representations of bulk bands, eliminating the need for large-scale vortex simulations. Exploiting this approach, we uncover a striking yet natural prediction: even conventional s-wave superconductors with trivial atomic-limit bands can host vortex Majorana modes. Our theory establishes a unified and computationally efficient foundation for high-throughput ab initio screening of superconductors with exotic vortex topological phenomena.