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Experimental Evidence of Cage Conduction Bands in Superconducting Cement 12CaO$\cdot$7Al$_2$O$_3$

Natural 12CaO$\cdot$7Al$_2$O$_3$ (C12A7) is a wide bandgap insulator, but conductivity can be realized by introducing oxygen deficiency. Currently, there are two competing models explaining conductivity in oxygen-deficient C12A7, one involving the electron transfer via a "cage conduction band" inside the nominal band gap, the other involving electron hopping along framework lattice sites. To help resolve this debate, we probe insulating and conducting C12A7 with X-ray emission, X-ray absorption, and X-ray photoemission spectroscopy, which provide a full picture of both the valence and conduction band edges in these materials. These measurements suggest the existence of a narrow conduction band between the main conduction and valence bands common in both conducting and insulating C12A7 and support the theory that free electrons in oxygen-deficient C12A7 occupy the low-energy states of this narrow band. Our measurements are corroborated with density functional theory calculations.