Superconductivity in $\beta$-pyrochlore superconductor KOs$_{2}$O$_{6}$: treatment within strong-coupling Eliashberg theory

TL;DR

This paper investigates how rattling phonons affect superconductivity in the $eta$-pyrochlore KOs$_{2}$O$_{6}$ using strong-coupling Eliashberg theory, revealing a discontinuous phonon frequency change at the phase transition and its impact on the superconducting gap.

Contribution

It introduces a detailed Eliashberg analysis incorporating temperature-dependent phonon spectra to explain the phase transition effects on superconductivity in KOs$_{2}$O$_{6}$.

Findings

Discontinuous change in rattling phonon frequency at the phase transition.

Altered temperature dependence of the superconducting gap.

Consistency with recent experimental observations.

Abstract

We study the influence of the rattling phonons on superconductivity in $\beta$-pyrochlore KOs$_{2}$O$_{6}$ compound based on the strong-coupling Eliashberg approach. In particular, analyzing the specific heat data we find that the rattling phonon frequency changes discontinuously at the critical temperature of the first order phase transition. Solving the strong-coupling Eliashberg equations with temperature dependent $\alpha^{2}F(\omega)$, we investigate the consequence of this first order phase transition for the anomalous temperature dependence of the superconducting gap. We discuss our results in context of the recent experimental data.