We have measured the reflectivity of the optimally doped ${\mathrm{Ca}}_{8.5}{\mathrm{La}}_{1.5}\left({\mathrm{Pt}}_3{\mathrm{As}}_8\right)\left({\mathrm{Fe}}_{10}{\mathrm{As}}_{10}\right)$ single crystal $\left(T_c=32.8\mathrm{K}\right)$ over the broad frequency range from $40{\text{cm}}^{-1}$ to 12 $000{\text{cm}}^{-1}$ and for temperatures from 8 K to 300 K. The optical conductivity spectra of the low-frequency region $\left(<1000{\text{cm}}^{-1}\right)$ in the normal state (80 K $<T\le 300$ K) is well fitted with two Drude forms, which indicates the presence of multiple bands at the Fermi level. Decreasing temperature below 80 K, this low-frequency Drude spectra develops a pseudogap (PG) hump structure at around $100{\text{cm}}^{-1}$ and continuously evolves into the fully opened superconducting (SC) gap structure below $T_c$. Theoretical calculations of the optical conductivity with the preformed Cooper pair model provide an excellent description of the temperature evolution of the PG structure above $T_c$ into the SC gap structure below $T_c$. The extracted two SC gap sizes are ${\mathrm{\Delta }}_S=4.9$ $\text{meV}$ and ${\mathrm{\Delta }}_L=14.2$ $\text{meV}$, suggesting ${\mathrm{Ca}}_{8.5}{\mathrm{La}}_{1.5}\left({\mathrm{Pt}}_3{\mathrm{As}}_8\right)\left({\mathrm{Fe}}_{10}{\mathrm{As}}_{10}\right)$ as a multiple-gap superconductor with a mixed character of the weak-coupling and strong-coupling superconductivity.

• Received 30 November 2016
• Revised 28 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.094510