Phonon structure in point-contact spectra of MgB$_2$

TL;DR

This paper investigates the phonon features in point-contact spectra of MgB$_2$, emphasizing the role of self-energy effects in strong-coupling superconductors with short electron mean free paths, and compares theoretical models with experimental data.

Contribution

It provides a comparative analysis of nonlinear conductivity expressions for different contact regimes and relates them to phonon structures observed in MgB$_2$ point-contact spectra.

Findings

Expressions for nonlinear conductivity are similar across contact types.

Phonon structures are observed in the $ ext{pi}$-band spectra.

Self-energy effects significantly influence spectral features.

Abstract

In strong-coupling superconductors with a short electron mean free path the self-energy effects in the superconducting order parameter play a major role in the phonon manifestation of the point-contact spectra at above-gap energies. We compare the expressions for the nonlinear conductivity of tunnel, ballistic, and diffusive point-contacts and show that these expression are similar and correspond to the measurements of the phonon structure in the point-contact spectra for the $\pi$-band of MgB$_{2}$.