Scaling of the Fano effect of the in-plane Fe-As phonon and the superconducting critical temperature in Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$

TL;DR

This study uses infrared spectroscopy to explore how the Fano effect of the in-plane Fe-As phonon correlates with superconductivity in Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$, revealing a linear relationship with critical temperature.

Contribution

It uncovers a linear correlation between the Fano parameter and superconducting temperature, linking phonon-electron coupling to superconductivity in this material.

Findings

The Fano parameter $1/q^2$ is sensitive to magnetic and structural orderings.

A linear correlation exists between $1/q^2$ and $T_c$ in the paramagnetic state.

A sizable $xy$ orbital component is crucial for the Fano effect and possibly for pairing.

Abstract

By means of infrared spectroscopy we determine the temperature-doping phase diagram of the Fano effect for the in-plane Fe-As stretching mode in Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$. The Fano parameter $1/q^2$, which is a measure of the phonon coupling to the electronic particle-hole continuum, shows a remarkable sensitivity to the magnetic/structural orderings at low temperatures. More strikingly, at elevated temperatures in the paramagnetic/tetragonal state we find a linear correlation between $1/q^2$ and the superconducting critical temperature $T_c$. Based on theoretical calculations and symmetry considerations, we identify the relevant interband transitions that are coupled to the Fe-As mode. In particular, we show that a sizable $xy$ orbital component at the Fermi level is fundamental for the Fano effect and possibly also for the superconducting pairing.