Ab initio probing of the electronic band structure and Fermi surface of fluorine-doped WO$_3$ as a novel low-$T_C$ superconductor

First-principles calculations were performed to investigate the electronic structure and the Fermi surface of the newly discovered low-temperature superconductor: fluorine-doped WO$_3$. We find that F doping provides the transition of the insulating tungsten trioxide into a metallic-like phase WO$_{3-x}$F$_x$, where the near-Fermi states are formed mainly from W $5d$ with admixture of O $2p$-orbitals. The cooperative effect of fluorine additives in WO$_3$ consists in change of electronic concentration as well as the lattice constant. At probing their influence on the near-Fermi states separately, the dominant role of the electronic factor for the transition of tungsten oxyfluoride into superconducting state was established. The volume of the Fermi surface gradually increases with the increase of the doping. In the sequence WO$_3\to{}$WO$_{2.5}$F$_{0.5}$ the effective atomic charges of W and O ions decrease, but much less, than it is predicted within the idealized ionic model – owing to presence of the covalent interactions W–O and W–F.