Combined effect of 13C isotope and vacancies on the phonon properties in AB stacked bilayer graphene

Abstract

The combined effects of 13C isotope and vacancies on the phonon properties in AB stacked bilayer graphene (BLG) are explored theoretically. We have calculated the phonon density of states (PDOS) by varying the isotope contents (0–100%) and vacancies (0–30%) in both layers and only in the upper layer of the BLG using forced vibrational method. We found that both isotope and vacancy or merging of these two defects significantly affect the PDOS, especially, E2g mode phonon, which is responsible for the Raman G band, shifted downward with the increase of defect concentrations. Moreover, when 13C isotopes are induced only in the upper layer, E2g peak splits into two peaks which corresponds well with the experimental results of 13C/12C dependence G peak splitting in the Raman spectra of BLG. We also explored the defect induced phonon localization in BLG. Our calculated typical mode patterns show that high frequency optical phonons are strongly localized in the vacancy as well as merging 13C isotope and vacancy defected BLG. The calculated average localization length noticed that strong phonon localization exists at 60% 13C isotope concentration. These findings are important for understanding the experimentally observed Raman spectra as well as thermal transport in BLG.