Revisiting optical properties of MgB$_{2}$ with a high-quality sample prepared by a HPCVD method

We investigated a high-quality MgB$_{2}$ thin film with a thickness of $\sim$1000 nm on an Al$_{2}$O$_{3}$ substrate using optical spectroscopy. We measured the reflectance spectra of the film at various temperatures both below, and above, the superconducting transition temperature, $T_c$ $\simeq$ 40 K. An earlier study showed that when the sample surface is exposed to air the optical properties of the surface change immediately, however, the saturated change is negligibly small in the far-infrared region. The optical conductivity spectrum in the normal state shows two (narrow and broad) Drude modes, with the narrow Drude mode being dominant in the low frequency region below 1000 cm$^{-1}$. Our study, which uses a good-quality sample, provides more reliable data on the optical properties of MgB$_2$, in a similar spectral range. The optical data is analyzed further using an extended Drude model, and the electron-phonon spectral density function, $\alpha^2F(\omega)$, is extracted. The spectral density function $\alpha^2F(\omega)$ features two peaks: a small one near 114 cm$^{-1}$, and a strong peak around the 550 cm$^{-1}$ where the B-B bond stretching phonon exists. Our data in the superconducting state does not show the expected energy shift of the onset of scattering associated with the $\alpha^2F(\omega)$ peaks.