Vacancy-induced in-gap states in sodium tungsten bronzes: Density functional investigations

We have performed extensive ab-initio self-consistent electronic-structure calculations on WO3 and NaWO3 with single- and double-oxygen-vacancy defects within the framework of density functional theory. Our calculated density of states reveals that the in-gap states in WO3 and NaWO3 are the consequence of oxygen vacancies in the system. The evolution of the induced states occurs from the unpaired electrons donated by the oxygen vacancy. We found that the energy positions of the in-gap states are sensitive to the oxygen vacancy concentrations. The in-gap states in NaWO3 are formed close to the valence band, which are pushed towards the conduction band with the increase in oxygen vacancies, whereas the states are formed mostly in the mid-gap region in the WO3 system. Our finding can now well explain the discrepancy in experimental band dispersion measurements from ARPES with that of WO3 and NaWO3 band calculations