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Rutile TiO2 is a paradigmatic transition metal oxide with applications inoptics, electronics, photocatalysis, etc., that are subject to pervasiveelectron-phonon interaction. To understand how energies of its electronicbands, and in general semiconductors or metals where the frontier orbitals havea strong d-band character, depend on temperature, we perform a comprehensivetheoretical and experimental study of the effects of electron-phonon (e-p)interactions. In a two-photon photoemission (2PP) spectroscopy study we observean unusual temperature dependence of electronic band energies within theconduction band of reduced rutile TiO2, which is contrary to the wellunderstood sp-band semiconductors and points to a so far unexplained dichotomyin how the e-p interactions affect differently the materials where the frontierorbitals are derived from the sp- and d-orbitals. To develop a broadlyapplicable model, we employ state-of-the-art first-principles calculations thatexplain how phonons promote interactions between the Ti-3d orbitals of theconduction band within the octahedral crystal field. The characteristicsdifferences in e-p interactions experienced by the Ti 3d-orbitals of rutileTiO2 crystal lattice are contrasted with the more familiar behavior of the Si2s-orbitals of stishovite SiO2 polymorph, in which the frontier 2s-orbitalexperience a similar crystal field with the opposite effect...

Electron-phonon coupling in d-electron solids: A temperature dependent study of rutile TiO2 by first-principles theory and two-photon photoemission