# Anomalous Anisotropic Exciton Temperature Dependence in Rutile TiO2

## TL;DR

This study reveals an unusual anisotropic temperature-dependent behavior of excitonic peaks in rutile TiO2, showing a blueshift along the a-axis and a redshift along the c-axis due to electron-phonon interactions.

## Contribution

It provides an ab initio analysis of anisotropic electron-phonon coupling effects on excitons in rutile TiO2, highlighting the origin of the anomalous blueshift.

## Key findings

- Anisotropic temperature dependence of excitonic peaks in rutile TiO2.
- Identification of two electron-phonon interaction terms causing the blueshift.
- Methodology enables complete ab initio treatment of electron-phonon effects in polar materials.

## Abstract

Elucidating the details of the electron-phonon coupling in semiconductors and insulators is a topic of pivotal interest, as it governs the transport mechanisms and is responsible for various phenomena such as spectral-weight transfers to phonon sidebands and self-trapping. Here, we investigate the influence of the electron-phonon interaction on the excitonic peaks of rutile TiO$_2$, revealing a strong anisotropic polarization dependence with increasing temperature, namely an anomalous blueshift for light polarized along the a-axis and a conventional redshift for light polarized along the c-axis. By employing many-body perturbation theory, we identify two terms in the electron-phonon interaction Hamiltonian that contribute to the anomalous blueshift of the a-axis exciton. Our approach paves the way to a complete ab initio treatment of the electron-phonon interaction and of its influence on the optical spectra of polar materials.