Reconciling the theoretical and experimental electronic structure of NbO2

Metal-insulator transition materials such as ${\mathrm{NbO}}_{2}$ have generated much excitement in recent years for their potential applications in computing and sensing. ${\mathrm{NbO}}_{2}$ has generated considerable debate over the nature of the phase transition and the values of the band gap and bandwidths in the insulating phase. We present a combined theoretical and experimental study of the band gap and electronic structure of the insulating phase of ${\mathrm{NbO}}_{2}$. We carry out ab initio density functional theory (DFT) plus $U$ calculations, directly determining the $U$ and $J$ parameters for both the Nb $4d$ and O $2p$ subspaces through the recently introduced minimum-tracking linear response method. We find a fundamental bulk band gap of 0.80 eV for the full $\mathrm{DFT}+U+J$ theory. We also perform calculations and measurements for a (100)-oriented thin film. Scanning tunneling spectroscopy measurements show that the surface band gap varies from 0.75 to 1.35 eV due to an excess of oxygen in and near the surface region of the film. Slab calculations indicate metallicity localized at the surface region caused by an energy level shift consistent with a reduction in Coulomb repulsion. We demonstrate that this effect in combination with the simple, low-cost $\mathrm{DFT}+U+J$ method can account for the bandwidths and $p\text{\ensuremath{-}}d$ gap observed in x-ray photoelectron spectroscopy experiments. Overall, our results indicate the possible presence of a two-dimensional anisotropic metallic layer at the (100) surface of ${\mathrm{NbO}}_{2}$.