Phonon singularities on volt-ampere curves of niobium point contacts

TL;DR

This study investigates phonon-related features in volt-ampere curves of niobium point contacts at low temperatures, revealing singularities in superconducting states linked to inelastic electron transitions between Cooper pair potentials.

Contribution

It demonstrates the presence of phonon singularities in superconducting niobium point contacts and links these to inelastic electron transitions, expanding understanding of electron-phonon interactions in such systems.

Findings

Singularities appear in superconducting state I-V curves.

No phonon spectra detected in dirty normal contacts.

Singularities are due to inelastic electron transitions between Cooper pair potentials.

Abstract

The volt-ampere curves and their second derivatives were studied for niobium point contacts at low temperatures in the voltage range corresponding to the characteristic phonon energies. It was found that while for the dirty contacts in the normal state no PC spectra of phonons could be detected, in the superconducting state there were singularities in the I-V curves corresponding to maxima either in the first or in the second derivatives. The singularities observed were due to the energy dependence of the excess current. We suppose that the origin of these singularities is due to the inelastic transitions of electrons between chemical potentials of Cooper pairs at both sides of the contact, which differ in energy by $eV$. These transitions are possible if $\xi \left(0 \right)\gtrsim d \sim{{\Lambda}_{\varepsilon}}$ ($\xi (0)$ being the coherence length, $d$, the contact diameter, ${{\Lambda}_{\varepsilon}}={{({{l}_{i}}\cdot {{l}_{\varepsilon}})}^{1/2}}$, where ${{l}_{i}}$ and ${{l}_{\varepsilon}}$ being the elastic and inelastic electron mean free paths, respectively).