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

Abstract

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.

Theoretical and experimental study of temperature effect on electronic and optical properties of TiO₂: Comparing rutile and anatase

“…For rutile TiO 2 , several studies of temperature effects have been reported. Shang et al examined temperature renormalization effects on the t 2g and e g bands in rutile TiO 2 using first-principles and two-photon photoemission spectroscopy measurements [28]. In another study, the elementary excitations in rutile TiO 2 showed anisotropic exciton temperature dependence due to electron-phonon interactions [29].…”

Photoexcitation of bulk polarons in rutile TiO2

“…The R-R110 2PPE spectrum was recorded after the sample cooled to 300 K following sample preparation (detailed in the SM [22]). Accurate monitoring of the sample temperature is important as temperature is known to affect 2PPE spectra of TiO 2 [23]. Surface O vac will readily react with residual UHV water; however, the chamber base pressure of 1×10 -10 mbar ensures the slow rate of hydroxylation within the time required to record the R-R110 spectrum in Fig.…”

Link between Structural and Optical Properties of CoxFe3–xO4 Nanoparticles and Thin Films with Different Co/Fe Ratios

“…In most semiconductors, the valence band maximum (VBM) is formed by p-orbitals, while the conduction band minimum (CBM) consists of s-orbitals. In d-orbital-derived bands, such as the valence band and the conduction band in Co x Fe 3– x O 4 , band-energy shifts with temperature are expected, either to higher or lower energy depending on the surrounding ligand field . Thus, an emission with participation of the valence or the conduction band should show a distinct shift with temperature.…”

“…In dorbital-derived bands, such as the valence band and the conduction band in Co x Fe 3−x O 4 , band-energy shifts with temperature are expected, either to higher or lower energy depending on the surrounding ligand field. 82 Thus, an emission with participation of the valence or the conduction band should show a distinct shift with temperature. Figure 4 summarizes the outcome of temperature-resolved PL measurements on Co 0.9 Fe 2.1 O 4 nanoparticles.…”