FeTe$_{0.55}$Se$_{0.45}$: a multiband superconductor in the clean and dirty limit

The detailed optical properties of the multiband iron-chalcogenide superconductor FeTe$_{0.55}$Se$_{0.45}$ have been reexamined for a large number of temperatures above and below the critical temperature $T_c=14$ K for light polarized in the a-b planes. Instead of the simple Drude model that assumes a single band, above $T_c$ the normal-state optical properties are best described by the two-Drude model that considers two separate electronic subsystems; we observe a weak response ($\omega_{p,D;1}\simeq 3000$ cm$^{-1}$) where the scattering rate has a strong temperature dependence ($1/\tau_{D,1}\simeq 32$ cm$^{-1}$ for $T \gtrsim T_c$), and a strong response ($\omega_{p,D;2}\simeq 14\,500$ cm$^{-1}$) with a large scattering rate ($1/\tau_{D,2}\simeq 1720$ cm$^{-1}$) that is essentially temperature independent. The multiband nature of this material precludes the use of the popular generalized-Drude approach commonly applied to single-band materials, implying that any structure observed in the frequency dependent scattering rate $1/\tau(\omega)$ is spurious and it cannot be used as the foundation for optical inversion techniques to determine an electron-boson spectral function $\alpha^2 F(\omega)$. Below $T_c$ the optical conductivity is best described using two superconducting optical gaps of $2\Delta_1\simeq 45$ and $2\Delta_2 \simeq 90$ cm$^{-1}$ applied to the strong and weak responses, respectively. The scattering rates for these two bands are vastly different at low temperature, placing this material simultaneously in both clean and dirty limit. Interestingly, this material falls on the universal scaling line initially observed for the cuprate superconductors.