# Oxygen-vacancy driven electron localization and itinerancy in rutile-based TiO$_2$

## TL;DR

This study combines advanced computational methods to explore how oxygen vacancies influence electron localization and itinerancy in rutile TiO₂, revealing complex correlation effects and phase behavior.

## Contribution

It provides a detailed theoretical analysis of oxygen vacancy effects on electronic structure and correlations in TiO₂ using DFT+DMFT, highlighting the role of charge localization and phase stability.

## Key findings

- Isolated oxygen vacancies do not metallize TiO₂ at low temperatures.
- In-gap states are identified consistent with experimental data.
- Higher vacancy concentrations stabilize a correlated metallic phase.

## Abstract

Oxygen-deficient TiO$_2$ in the rutile structure as well as the Ti$_3$O$_5$ Magn{\'e}li phase is investigated within the charge self-consistent combination of density functional theory (DFT) with dynamical mean-field theory (DMFT). It is shown that an isolated oxygen vacancy (V$_{\rm O}$) in titanium dioxide is not sufficient to metallize the system at low temperatures. In a semiconducting phase, an in-gap state is identified at $\varepsilon_{\rm IG}^{\hfill}\sim -0.75\,$eV\, in excellent agreement with experimental data. Band-like impurity levels, resulting from a threefold V$_{\rm O}$-Ti coordination as well as entangled $(t_{2g},e_g)$ states, become localized due to site-dependent electronic correlations. Charge localization and strong orbital polarization occur in the V$_{\rm O}$-near Ti ions, which details can be modified by a variation of the correlated subspace. At higher oxygen vacancy concentration, a correlated metal is stabilized in the Magn{\'e}li phase. A V$_{\rm O}$-defect rutile structure of identical stoichiometry shows key differences in the orbital-resolved character and the spectral properties. Charge disproportionation is vital in the oxygen-deficient compounds, but obvious metal-insulator transitions driven or sustained by charge order are not identified.