# First-Principles Study of Localised and Delocalised Electronic States in Crystallographic Shear Phases of Niobium Oxide

## TL;DR

This study uses first-principles calculations to analyze the electronic structure and magnetism of niobium oxide shear phases, revealing coexistence of localized and delocalized states influenced by their block structures.

## Contribution

It provides a detailed theoretical understanding of electronic localization and magnetic properties in niobium oxide shear phases, highlighting the importance of advanced functionals for accurate descriptions.

## Key findings

- Flat bands indicate localized electrons in niobium oxide structures.
- Delocalized electrons contribute to metallic behavior beyond a certain doping threshold.
- Localized and delocalized states are effectively one-dimensional and site-dependent.

## Abstract

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-Nb$_2$O$_5$, Nb$_{25}$O$_{62}$, Nb$_{47}$O$_{116}$, Nb$_{22}$O$_{54}$, and Nb$_{12}$O$_{29}$. 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 localised and delocalised electronic states. Electrons localise in orbitals spanning multiple niobium sites in the plane of the blocks. Localised and delocalised electronic states are both effectively one-dimensional and are partitioned between different types of niobium sites. Flat bands associated with localised electrons are present even at the GGA level, but a correct description of the localisation 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 behaviour is similar to that of $n$-doped semiconductors, but with a limited capacity for localised electrons. When a threshold of one electron per block is exceeded, metallic electrons are added to existing localised electrons. We propose that this behaviour 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.