Euler Topology in Superconducting Honeycomb Lattices

Electronic bands in systems with space–time inversion (IST) symmetry can host nontrivial Euler topology. Here, we investigate the band topology of IST-symmetric superconducting honeycomb lattices and demonstrate that s-wave spin–singlet (SWSS) and f-wave spin–triplet (FWST) superconducting pairings give rise to valley-Euler and Euler superconductors, respectively. We find that Euler topology in both pairing states gives rise to mirror-symmetry-protected helical Andreev bound states at superconducting domain walls. Furthermore, we show that Euler topology in the FWST state induces non-Abelian braiding of Dirac nodes in momentum space when anisotropic hopping is introduced. Our work establishes band engineering combined with superconducting electronic instabilities as a natural route to realizing nontrivial Euler band topology and its domain-wall physics in Dirac materials.