Unravelling the mechanism of the semiconducting-like behavior and its relation to superconductivity in (CaFe$_{1-x}$Pt$_{x}$As)$_{10}$Pt$_{3}$As$_{8}$

The temperature-dependence of the in-plane optical properties of (CaFe$_{1-x}$Pt$_{x}$As)$_{10}$Pt$_{3}$As$_{8}$ have been investigated for the undoped ($x=$0) parent compound, and the optimally-doped ($x=$0.1) superconducting material ($T_{c}\simeq$ 12 K) over a wide frequency range. The optical conductivity has been described using two free-carrier (Drude) components, in combination with oscillators to describe interband transitions. At room temperature, the parent compound may be described by a strong, broad Drude term, as well as a narrow, weaker Drude component. Below the structural and magnetic transitions at $\simeq$ 96 and 83 K, respectively, strength is transferred from the free-carrier components into a bound excitation at $\simeq$ 1000 cm$^{-1}$, and the material exhibits semiconducting-like behavior. In the optimally-doped sample, at room temperature the optical properties are again described by narrow and broad Drude responses comparable to the parent compound; however, below $T^\ast \simeq$ 100 K, strength from the narrow Drude is transferred into a newly-emergent low-energy peak at $\simeq$ 120 cm$^{-1}$, which arises from a localization process, resulting in semiconducting-like behavior. Interestingly, below $T_{c}$, this peak also contributes to the superfluid weight, indicating that some localized electrons condense into Cooper pairs; this observation may provide insight into the pairing mechanism in iron-based superconductors.