Localized and delocalized electrons in room-temperature stable electride [Ca₂₄Al₂₈O₆₄]⁴⁺(O^2-) _2-x(e^-)_2x: Analysis of optical reflectance spectra

[Ca₂₄Al₂₈O₆₄]⁴⁺(O ^2-)_2-x(e^-)_2x (O ≤ x ≤ 2, C12A7:e^-) crystal shows a metal-insulator transition at x ∼ 1. Varied concentrations of electrons (N_e) are introduced in the subnanometer-sized crystallographic cages of [Ca₂₄Al ₂₈O₆₄]⁴⁺(O^2-)₂ (12CaO·7Al₂O₃, C12A7) in place of the O ^2- ions accommodated in the cages. The optical reflectance spectra of C12A7:e^- crystals were analyzed using the Drude-Lorentz model to examine the electronic states and carrier transport mechanisms experimentally. The concentrations of localized electrons trapped in the cages were estimated from Lorentz-type optical responses around 0.4 and 2.8 eV, and those of delocalized electrons from a Drude-type response. C12A7:e^- with N_e lower than 5 × 10²⁰ cm^-3 (x ∼ 0.5) shows polaronic hopping conduction and its reflectance spectrum shows only the Lorentz-type responses. The Drude-type response starts to appear when N _e exceeds 5 × 10²⁰, and coexists with the Lorentz-type responses at N_e between 5 × 10²⁰ and 2 × 10²¹ cm^-3 (x ∼ 2), which indicates that the localized electrons coexist with the delocalized electrons even in the metallic samples. These results support previous theoretical studies proposing that a strong electron-lattice interaction deforms the soft cage structure of C12A7, and forming an insulating state at the low N_e limit, while the cage deformation is reduced at the high N_e limit, leading to the insulator-metal transition.