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Correlation of electron-phonon in cubic zirconia: $G_0W_0 @DFPT$ scheme

The indirect carrier-phonon vertex function is evaluated for cubic zirconia by employing the many-body perturbation theory on top of the frozen phonon model. The phonon-induced carrier velocity and spectral renormalization are represented at each individual lattice vibronic mode. Our results show that for the indirect electron-phonon scattering, optical phonons make up the dominant contribution. It is observed that, despite the phonon-phonon interaction, there is a substantial polaronic character for all the activated lattice optical vibrations which is in accordance with the previous experimental and theoretical finding concerning the crucial role of optical phonons. Eventually our results are capable to discuss that, in the presence of optical phonons a transition between small to large polaron is probable