Electronic correlations and superconducting response in the optical properties of FeTe$_{\mathbf{0.55}}$Se$_{\mathbf{0.45}}$

The in-plane complex optical properties of the iron-chalcogenide superconductor FeTe$_{0.55}$Se$_{0.45}$ have been determined above and below $T_c = 14$~K. At room temperature the conductivity is described by a weakly-interacting Fermi liquid with $\omega_{p,D}\simeq 7200$~cm$^{-1}$ and $1/\tau_D\simeq 414$~cm$^{-1}$. Below 100~K the conductivity is no longer described by the Drude model. Adopting the generalized Drude model reveals that $1/\tau(\omega) \propto \omega$ in the terahertz region just above $T_c$, signaling the increasingly correlated nature of this material.\footnote{C. C. Homes {\em et al.}, Phys. Rev. B {\bf 81}, 180508(R) (2010).} For $T \ll T_c$ the superconducting plasma frequency $\omega_{p,S} \simeq 3000$~cm$^{-1}$ ($\lambda_{\it eff} \simeq 5300$~\AA ); $\omega_{p,S}^2/\omega_{p,D}^2 \ll 1$ indicating that this material is not in the clean limit. Allowing $\sigma_{dc}\equiv \sigma_1(\omega \rightarrow 0)$, then $\sigma_{dc}(T\simeq T_c) \simeq 3500\pm 400$ $\Omega^{-1}$cm$^{-1}$ and the superfluid density $\rho_{s0} \equiv \omega_{p,S}^2 \simeq 9\pm 1\times 10^6$~cm$^{-2}$ places material close to the scaling line $\rho_{s0}/8 \simeq 8.1\,\sigma_{dc}T_c$ for a BCS dirty-limit superconductor. Below $T_c$ the optical conductivity reveals two energy scales for the superconductivity at $\Delta_1(0) \simeq 2.5$~meV and $\Delta_2(0) \simeq 5.1$~meV, consistent with the $s^\pm$ model.