Bosonic excitation spectra of superconducting $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ and $\mathrm{YBa_2Cu_3O_{6+x}}$ extracted from scanning tunneling spectra

A detailed interpretation of scanning tunneling spectra obtained on unconventional superconductors enables one to gain information on the pairing boson. Decisive for this approach are inelastic tunneling events. Due to the lack of momentum conservation in tunneling from or to the sharp tip, those are enhanced in the geometry of a scanning tunneling microscope compared to planar tunnel junctions. This work extends the method of obtaining the bosonic excitation spectrum by deconvolution from tunneling spectra to nodal $d$-wave superconductors. In particular, scanning tunneling spectra of slightly underdoped $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ with a $T_c$ of $82\,\mathrm{K}$ and optimally doped $\mathrm{YBa_2Cu_3O_{6+x}}$ with a $T_c$ of $92\,\mathrm{K}$ reveal a resonance mode in their bosonic excitation spectrum at $\Omega_\mathrm{res} \approx 63\,\mathrm{meV}$ and $\Omega_\mathrm{res} \approx 61\,\mathrm{meV}$ respectively. In both cases, the overall shape of the bosonic excitation spectrum is indicative of predominant spin scattering with a resonant mode at $\Omega_\mathrm{res}<2\Delta$ and overdamped spin fluctuations for energies larger than $2\Delta$. To perform the deconvolution of the experimental data, we implemented an efficient iterative algorithm that significantly enhances the reliability of our analysis.