Vertex-corrected tunneling inversion in superconductors: Pb

TL;DR

This paper extends the McMillan-Rowell tunneling inversion method to include vertex corrections, improving the extraction of electron-phonon spectral functions from tunneling data, with application to lead (Pb).

Contribution

It introduces a vertex-corrected approach to tunneling inversion, accounting for lowest-order vertex corrections in superconductors.

Findings

Enhanced agreement with experimental Pb data.

Demonstrates the importance of vertex corrections in tunneling analysis.

Provides a more accurate spectral function extraction method.

Abstract

The McMillan-Rowell tunneling inversion program, which extracts the electron-phonon spectral function $\alpha^2F(\Omega)$ and the Coulomb pseudopotential $\mu^*$ from experimental tunneling data, is generalized to include the lowest-order vertex correction. We neglect the momentum dependence of the electron-phonon matrix elements, which is equivalent to using a local approximation. The perturbation theory is performed on the imaginary axis and then an exact analytic continuation is employed to produce the density of states on the real axis. Comparison is made with the experimental data for Pb.