Temperature dependence of disorder sensitivity of phonon modes in finite-gap materials

The correlation between electronic disorder (quantified by the Urbach energy ${E}_{U}$) and phonon linewidth $(\mathrm{\ensuremath{\Gamma}})$ is known to be linear. However, both parameters exhibit temperature dependence, raising the question of whether the slope of the $\mathrm{\ensuremath{\Gamma}}$ vs ${E}_{U}$ plot remains constant with temperature. In this study, we investigate temperature dependence of the slope, denoted as $\ensuremath{\xi}$, which represents the sensitivity of phonon mode to changes in disorder. By applying theoretical models for the temperature dependence of $\mathrm{\ensuremath{\Gamma}}$ and ${E}_{U}$, we derive an expression for $\ensuremath{\xi}(T)$, revealing its nonlinear behavior at varying temperatures. Our analysis, based on Raman and optical absorption spectra of ${\mathrm{EuFeO}}_{3}$, demonstrates the explicit temperature dependence of $\ensuremath{\xi}$. This provides insights into the disorder sensitivity of vibrational modes, which is crucial for understanding phonon dynamics and transport properties. The findings are further supported by additional investigations on ${\mathrm{TiO}}_{2}$, emphasizing the utility of combined optical and Raman spectroscopic techniques in probing phonon-resolved disorder sensitivity in materials with finite bandgap where ${E}_{U}$ can be observed.