Euler Topology in Superconducting Honeycomb Lattices

TL;DR

This paper explores how superconducting honeycomb lattices with IST symmetry can host nontrivial Euler topologies, leading to protected edge modes and non-Abelian braiding phenomena.

Contribution

It demonstrates that specific superconducting pairings induce Euler topology and associated exotic phenomena in honeycomb lattices with IST symmetry.

Findings

Euler topology leads to mirror-symmetry-protected helical domain-wall modes

FWST pairing induces non-Abelian braiding of Dirac nodes

Superconducting instabilities can realize nontrivial Euler band topology

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.