First-principles study of localized and delocalized electronic states in crystallographic shear phases of niobium oxide

Crystallographic shear phases of niobium oxide form an interesting family of compounds that have received attention both for their unusual electronic and magnetic properties, as well as their performance as intercalation electrode materials for lithium-ion batteries. Here we present a first-principles density-functional theory study of the electronic structure and magnetism of H-Nb₂O₅, Nb₂₅O₆₂, Nb₄₇O₁₁₆, Nb₂₂O₅₄, and Nb₁₂O₂₉. These compounds feature blocks of niobium-oxygen octahedra as structural units, and we show that this block structure leads to a coexistence of flat and dispersive energy bands, corresponding to localized and delocalized electronic states. Electrons localize in orbitals spanning multiple niobium sites in the plane of the blocks. Localized and delocalized electronic states are both effectively one-dimensional and are partitioned between different types of niobium sites. Flat bands associated with localized electrons are present even at the GGA level, but a correct description of the localization requires the use of GGA+U or hybrid functionals. We discuss the experimentally observed electrical and magnetic properties of niobium suboxides in light of our results, and argue that their behavior is similar to that of n-doped semiconductors, but with a limited capacity for localized electrons. When a threshold of one electron per block is exceeded, metallic electrons are added to existing localized electrons. We propose that this behavior of shear phases is general for any type of n-doping, and should transfer to doping by alkali metal (lithium) ions during operation of niobium oxide-based battery electrodes. Future directions for theory and experiment on mixed-metal shear phases are suggested.