Polaronic correlation offsets in tetrahedral semiconductors

• Using GW and Migdal approximations, electron and phonon self-energies are calculated for diamond and silicon crystal
• Phonon-induced renormalization factor is evaluated for both crystal, particularly near the band edges.
• Raising the temperature makes considerable transition from Fan term to Debye–Waller perturbation of electron energies.
• Polaronic behavior for diamond due to the strong electron–phonon coupling is inferred from carrier velocity renormalizations.

Employing the first principle calculation combined with many-body perturbation theory, the carrier–phonon vertex function is evaluated in tetrahedral semiconductor silicon and diamond crystal. Moreover, the phonon induced quasiparticle spectral renormalization factors, phonon line-widths and carrier velocity renormalizations are evaluated at different temperatures. Our results illustrate a pronounced difference between the degree of carrier coupling to phonon satellite in silicon and diamond by analysis of the rates of thermalization. Particularly, for diamond, the large amount of renormalization is an indication of strong polaronic nature, which is in good agreement with experimental and theoretical studies, which prove the significant role of electron phonon coupling. Further, going to the higher temperatures makes considerable deviation from first-order phonon-induced to the second-order phonon perturbation of electron energies. Our study suggests for the significant contribution of electron–phonon self-energy in the electronic-related features of carbon-based rather than silicon-based materials.

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