Non-adiabatic phonons in highly-doped graphene

U ovom radu, ispituje se valjanost upotrebe adijabatske Born-Oppenheimer aproksimacije kod opisa interakcije elektrona i jezgara u visoko dopiranom grafenu. Usporedbom rezultata modela čvrste veze i teorije funkcionala gustoće (DFT) za disperziju fonona dopiranog grafena, pokazuje se da adijabatski tretman fonona dovodi do velike renormalizacije E_2g fononskog moda u Γ točki, što nije ispravan rezultat. Kako bi se dobio ispravan vibracijski spektar, potrebno je uključiti dinamičke (neadijabatske) efekte elektron-fonon interakcije. Oni izazivaju velike promjene u dugovalnom dijelu vibracijskog spektra. Neadijabatska korekcija dobivena je kroz vlastitu energiju fonona, a efekt je dokazan i u DFT-u izračunom elektron-fonon interakcije. Metoda je zatim primijenjena na dopirani grafan. Dinamički efekti u dopiranom grafanu izraženiji su nego u dopiranom grafenu. In this seminar the validity of an adiabatic Born-Oppenheimer approximation in the description of electron-phonon interactions in highly doped graphene is examined. Comparing the tight - binding approximation model results and the ones obtained within density functional theory (DFT), it is shown that an adiabatic treatment of phonons leads to a huge renormalization of the E_2g phonon mode in the Brillouin zone center, which is an incorrect result. In order to obtain a correct vibration spectrum, dynamical (nonadiabatic) effects of an electron-phonon interaction should be taken into account. They produce non-negligible changes in the long-wave part of the spectrum. Nonadiabatic correction is obtained through phonon self-energy calculation, while its effect is proved also within a DFT calculation of electron-phonon interaction parameters. This method is then applied to doped graphane. Dynamical effects in doped graphane are more pronounced than in doped graphene.