Optical signatures of Euler superconductors

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>d</a:mi></a:math>-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.