  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.
