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Elucidating the details of the electron-phonon coupling in semiconductors andinsulators is a topic of pivotal interest, as it governs the transportmechanisms and is responsible for various phenomena such as spectral-weighttransfers to phonon sidebands and self-trapping. Here, we investigate theinfluence of the electron-phonon interaction on the excitonic peaks of rutileTiO$_2$, revealing a strong anisotropic polarization dependence with increasingtemperature, namely an anomalous blueshift for light polarized along the a-axisand a conventional redshift for light polarized along the c-axis. By employingmany-body perturbation theory, we identify two terms in the electron-phononinteraction Hamiltonian that contribute to the anomalous blueshift of thea-axis exciton. Our approach paves the way to a complete ab initio treatment ofthe electron-phonon interaction and of its influence on the optical spectra ofpolar materials.

Anomalous Anisotropic Exciton Temperature Dependence in Rutile TiO2