Optical conductivity of nonmetallic ${\mathrm{Ba}}_{0.69}$${\mathrm{K}}_{0.31}$${\mathrm{BiO}}_3$ single crystals: Evidence for bipolaron formation

We report the far-infrared to near-ultraviolet reflectivity and ellipsometric measurements on an insulating ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{BiO}}_3$ single crystal, with a doping level x=0.31 just below the insulator-metal transition boundary. The optical conductivity was calculated using Kramers-Kronig analysis. We examine the experimental data in terms of a small bipolaron model. This model, with no free parameters, allows us to obtain a satisfactory agreement with our experimental results, including the overall shape and the peculiar temperature dependence of the optical conductivity. The same model provides a qualitative explanation for some aspects of the transport-measurement results reported previously.