Doping dependence of the optical properties ofBa1−xKxBiO3

We analyze the doping dependence of the optical conductivity of the ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\mathrm{Bi}{\mathrm{O}}_3$ (BKBO) system in the full doping range from $x=0\mathrm{}$ to $x=0.46\mathrm{}$. We have used the results of our reflectivity and ellipsometric measurements at $x=0.31, 0.38, 0.4, 0.46$, as well as the results obtained by other experimental groups at different doping levels, to analyze the doping dependence of the spectral weight distribution. At the insulator-metal transition boundary we observe the appearance of a Drude-like free-carrier peak in the optical conductivity. In the metallic phase, we have performed measurements in the normal as well as the superconducting state. The data show that BKBO becomes a better metal with increasing $x$ in the metallic regime due to a decrease in the scattering rate of the metallic charge carriers, while the density of the mobile (Drude) charge carriers does not significantly change with doping. The London penetration depth ${\lambda }_L$ is also found to be almost doping (and $T_c$) independent while the superconducting gap scales with $T_c$ as $\frac{2{\Delta }_s}{k_b{T}_c}=4.2\mathrm{}\pm 0.3$.