The band structure of WO₃ and non-rigid-band behaviour in Na_0.67WO₃ derived from soft x-ray spectroscopy and density functional theory

The electronic structure of single-crystal WO₃ and Na _0.67WO₃ (a sodium-tungsten bronze) has been measured using soft x-ray absorption and resonant soft x-ray emission oxygen K-edge spectroscopies. The spectral features show clear differences in energy and intensity between WO₃ and Na_0.67WO₃. The x-ray emission spectrum of metallic Na_0.67WO₃ terminates in a distinct Fermi edge. The rigid-band model fails to explain the electronic structure of Na_0.67WO₃ in terms of a simple addition of electrons to the conduction band of WO₃. Instead, Na bonding and Na 3s-O 2p hybridization need to be considered for the sodium-tungsten bronze, along with occupation of the bottom of the conduction band. Furthermore, the anisotropy in the band structure of monoclinic γ-WO₃ revealed by the experimental spectra with orbital-resolved geometry is explained via density functional theory calculations. For γ-WO₃ itself, good agreement is found between the experimental O K-edge spectra and the theoretical partial density of states of O 2p orbitals. Indirect and direct bandgaps of insulating WO₃ are determined from extrapolating separations between spectral leading edges and accounting for the core-hole energy shift in the absorption process. The O 2p non-bonding states show upward band dispersion as a function of incident photon energy for both compounds, which is explained using the calculated band structure and experimental geometry.