Angle-resolved photoemission spectroscopy of the metallic sodium tungsten bronzes $Na_{x}WO_{3}$

We have carried out high-resolution angle-resolved photoemission spectroscopy (ARPES) to study the electronic structure of highly metallic $Na_{x}WO_{3}$ (x=0.58, 0.65, 0.7, and 0.8). The experimentally determined valence-band structure has been compared with the results of an ab initio band-structure calculation. While the presence of an impurity band (level) induced by Na doping is often invoked to explain the insulating state found at low concentrations, we find no signature of impurity band (level) in the metallic regime. The states near E-Fare populated and the Fermi edge shifts rigidly with increasing electron doping (x). The linear dispersion of the conduction band explains the linear variation of thermodynamic properties including the specific heat and magnetic susceptibility. The presence of an electron-like Fermi surface at \Gamma(X) and its evolution with increasing Na content and the rigid shift of the Fermi level within creasing x agrees well with the band calculation