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$_{2}$

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 Ba1−xKxFe2As2. 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 Tc. 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.