Two-band conductivity of a FeSe$_{0.5}$Te$_{0.5}$ film by reflectance measurements in the terahertz and infrared range

We report an infrared spectroscopy study of a 200 nm thick FeSe$_{0.5}$Te$_{0.5}$ film grown on LaAlO$_3$ with T$_c$=13.7 K. We analyze the 20 K normal state absolute reflectance R$_N$ measured over a broad infrared range and the reflectance ratio R$_S$/R$_N$, R$_S$ being the superconducting state reflectance, measured at 6 K in the terahertz range down to 12 cm$^{-1}$. We show that the normal state model conductivity is given by two Drude components, one of which much broader and intense than the other. In the superconducting state, we find that a gap $\Delta$=37$\pm$3 cm$^{-1}$ opens up in the narrow Drude band only, while the broad Drude band results to be ungapped, at least in the explored spectral range. Our results show that only a two-band model can coherently describe both normal and superconducting state data.