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

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 $2Δ\approx 12$ 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 $λ\approx 0.2$, 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.