The Imaginary Part of the Optical Conductivity of $Ba_{1-x}K_xBiO_3$

TL;DR

This paper calculates and analyzes the imaginary part of the infrared conductivity in a superconductor, revealing features indicative of s-wave symmetry and providing insights into the electron-phonon coupling in Ba_{1-x}K_xBiO_3.

Contribution

It presents a detailed theoretical and experimental study of the imaginary conductivity in Ba_{1-x}K_xBiO_3, demonstrating its s-wave nature and small electron-phonon coupling.

Findings

Imaginary conductivity shows a minimum at twice the gap energy.

Experimental data confirms s-wave superconductivity in Ba_{1-x}K_xBiO_3.

Electron-phonon coupling constant is approximately 0.2.

Abstract

The frequency dependence of the imaginary part of the infrared conductivity is calculated for a superconductor. Sharp structure, characteristic of superconductivity with an order parameter with s-wave symmetry, appears in the BCS limit as a minimum at a frequency equal to twice the gap value. This structure scales with temperature but gets progressively smeared and shifted as impurity scattering is increased. The relationship between low frequency results and the zero frequency limit is investigated. Experimental results on $\BKBO$ are also presented. The low frequency imaginary part of the conductivity displays a minimum at $2\Delta \approx 12$ meV, and provides unequivocal evidence of an s-wave superconducting order parameter. Strong coupling (Eliashberg) results show similar trends. Using this formulation we find that the electron-phonon coupling in $\BKBO$ must necessarily be small, with coupling constant $\lambda \approx 0.2$, in agreement with conclusions drawn from measurements of the real part of the conductivity. Thus $\BKBO$ is an s-wave superconductor that is not driven by the electron-phonon interaction.