Anisotropic Drude response in Mg(B$_{1-x}$C$_{x})_{2}$

There exists an unsolved issue on MgB$_{2}$ that a plasma edge estimated from optical spectra so far is conspicuously inconsistent with a band calculation. It is mysterious since experimental band dispersions by ARPES are marvelously coincident with the band calculation. We report on a- and c-axis optical responses in Mg(B$_{1-x}$C$_{x})_{2 }$ using small single crystals and a FTIR spectrometer combined with an optical microscope. It was verified that the Drude responses show the anisotropy between a- and c-axis. The observed plasma frequencies $\omega_{p'}$ are considerably small compared to a theoretical value ($\sim $7eV), whereas the bare ones $\omega _p $, estimated from a sum rule of optical conductivity $\int {d\omega \sigma (\omega )=(\pi /2)\omega _p^2 } =(\pi /2)\varepsilon _\infty \omega _p^{'2} $, are fairly coincident with it. We also discuss an effect of carbon-substitution on carrier concentration and scattering rate in a multiband system. This work was supported by the New Energy and Industrial TechnologyDevelopment Organization(NEDO) through ISTEC as the Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.