Euler Topology in Superconducting Honeycomb Lattices

Abstract: 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 domain-wall modes. 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 superconducting electronic instabilities as a natural route to realizing nontrivial Euler band topology in Dirac materials.