Raman-Scattering Detection of Nearly Degenerate $s$-Wave and $d$-Wave Pairing Channels in Iron-Based ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ and ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ Superconductors

We show that electronic Raman scattering affords a window into the essential properties of the pairing potential $V_{\mathbf{k},{\mathbf{k}}^{\prime }}$ of iron-based superconductors. In ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ we observe band dependent energy gaps along with excitonic Bardasis-Schrieffer modes characterizing, respectively, the dominant and subdominant pairing channel. The $d_{x^2-y^2}$ symmetry of all excitons allows us to identify the subdominant channel to originate from the interaction between the electron bands. Consequently, the dominant channel driving superconductivity results from the interaction between the electron and hole bands and has the full lattice symmetry. The results in ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ along with earlier ones in $\mathrm{Ba}({\mathrm{Fe}}_{0.939}{\mathrm{Co}}_{0.061}{)}_2{\mathrm{As}}_2$ highlight the influence of the Fermi surface topology on the pairing interactions.