Electronic structure of sodium tungsten bronzes $Na_xWO_3$ by high-resolution angle-resolved photoemission spectroscopy

The electronic structure of sodium tungsten bronzes, $Na_xWO_3$, for full range of x is investigated by high resolution angle-resolved photoemission spectroscopy (HR-ARPES). The experimentally determined valence band structure has been compared with the results of ab initio band-structure calculation. The HR-ARPES spectra taken in both the insulating and metallic phase of $Na_xWO_3$ reveal the origin of metal-insulator transition (MIT) in the sodium tungsten bronze system. In the insulating $Na_xWO_3$, the near-EF states are localized due to the strong disorder caused by the random distribution of $Na^+$ ions in $WO_3$ lattice. While the presence of an impurity band (level) induced by Na doping is often invoked to explain the insulating state found at low concentrations, there is no signature of impurity band (level) found from our results. Due to disorder and Anderson localization effect, there is a long-range Coulomb interaction of conduction electrons; as a result, the system is insulating. In the metallic regime, the states near $E_F$ are populated and the Fermi level shifts upward rigidly with increasing electron doping (x). The volume of electronlike Fermi surface (FS) at the $\Gamma (X)$ point gradually increases with increasing Na concentration due to $W 5dt_2_g$ band filling. A rigid shift of $E_F$ is found to give a qualitatively good description of the FS evolution