Optical reflectivity of single-crystal ${\mathrm{Bi}}_2$${\mathit{M}}_3$${\mathrm{Co}}_2$${\mathrm{O}}_{9+\mathrm{\delta }}$ (M=Ca, Sr, and Ba) from the infrared to the vacuum-ultraviolet region

The dielectric functions of single-crystal ${\mathrm{Bi}}_2$ ${\mathit{M}}_3$ ${\mathrm{Co}}_2$ ${\mathrm{O}}_{9+\mathrm{\delta }}$ (M=Ca, Sr, and Ba) were obtained by optical-reflectivity measurements. The Bi-based Co oxides have a characteristic ${\mathrm{Bi}}_2$ ${\mathrm{O}}_2$ layer with two sheets of ${\mathrm{CoO}}_2$ plane per primitive cell, and can be a reference material for ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$. The obtained spectra are transformed to give the optical conductivity, and the optical properties of the ${\mathrm{CoO}}_2$ plane are discussed. Comparison of the electronic states of the Co and Cu oxides reveals two characteristics of high-${\mathit{T}}_{\mathit{c}}$ cuprates. One is that the peak of the midinfrared absorption seen in optical conductivity decreases in energy toward 0 eV upon doping. The other is that the doping-dependent excitation associated with the ${\mathrm{CuO}}_2$ plane is confined in the low-energy region and is separated from other excitations such as those in the ${\mathrm{Bi}}_2$ ${\mathrm{O}}_2$ layer.