Electron-phonon coupling in d-electron solids: A temperature-dependent study of rutile TiO_{2} by first-principles theory and two-photon photoemission

Abstract

Rutile TiO_{2} is a paradigmatic transition-metal oxide with applications in optics, electronics, photocatalysis, etc., that are subject to pervasive electron-phonon interaction. To understand how energies of its electronic bands, and in general semiconductors or metals where the frontier orbitals have a strong d-band character, depend on temperature, we perform a comprehensive theoretical and experimental study of the effects of electron-phonon (e-p) interactions. In a two-photon photoemission (2PP) spectroscopy study we observe an unusual temperature dependence of electronic band energies within the conduction band of reduced rutile TiO_{2}, which is contrary to the well-understood sp-band semiconductors and points to a so far unexplained dichotomy in how the e-p interactions affect differently the materials where the frontier orbitals are derived from the sp- and d orbitals. To develop a broadly applicable model, we employ state-of-the-art first-principles calculations that explain how phonons promote interactions between the Ti-3d orbitals of the conduction band within the octahedral crystal field. The characteristic difference in e-p interactions experienced by the Ti-3d orbitals of rutile TiO_{2} crystal lattice are contrasted with the more familiar behavior of the Si-2s orbitals of stishovite SiO_{2} polymorph, in which the frontier 2s orbital experiences a similar crystal field with the opposite effect. The findings of this analysis of how e-p interactions affect the d- and sp-orbital derived bands can be generally applied to related materials in a crystal field. The calculated temperature dependence of d-orbital derived band energies agrees well with and explains the temperature-dependent inter-d-band transitions recorded in 2PP spectroscopy of TiO_{2}. The general understanding of how e-p interactions affect d-orbital derived bands is likely to impact the understanding of temperature-dependent properties of highly correlated materials.