Optical signatures of Euler superconductors

TL;DR

This paper explores how multiband topological superconductors with a nontrivial Euler class exhibit unique optical responses, including a topological jump in optical conductivity and enhanced nonlinear effects, revealing observable signatures of their exotic topology.

Contribution

It introduces lattice models for non-Abelian Euler superconductors and demonstrates their distinctive optical responses, including topological jumps and nonlinear effects, extending understanding of topological superconductivity.

Findings

Topological jump in optical conductivity due to Euler class

Enhanced nonlinear currents in Euler superconductors

Generalization of results via diagrammatic approach

Abstract

We study optical manifestations of multigap band topology in multiband superconductors with a nontrivial topological Euler class. We introduce a set of lattice models for non-Abelian superconductors with the Euler invariant signified by a nontrivial quantum geometry. We then demonstrate that the topological Bogoliubov excitations realized in these models provide for a characteristic first-order optical response distinct from those of the other known topological superconductors. We find that the spectral distribution of the optical conductivity universally admits a topological jump originating from the Euler class in the presence of $d$-wave superconducting pairings, and naturally differs from the features induced by the quantum geometry in the noninteracting bands without pairing terms. Further to uncovering observable signatures in first-order optical conductivities, we showcase that the higher-order optical responses of the non-Abelian Euler superconductor can result in enhanced nonlinear currents that fingerprint the exotic topological invariant. Finally, by employing a diagrammatic approach, we generalize our findings beyond the specific models of Euler superconductors.