Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy
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Dresselhaus-2012-Effect of C-13 isotope doping on the optical phonon modes.pdf
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Author(s)
Rodriguez-Nieva, J. F.
Saito, R.
Costa, S. D.
Dresselhaus, Mildred
Date Issued
June 2012
Journal
Physical Review B
Publisher
American Physical Society
Citation
Rodriguez-Nieva, J. et al. “Effect of ^{13}C Isotope Doping on the Optical Phonon Modes in Graphene: Localization and Raman Spectroscopy.” Physical Review B 85.24 (2012). ©2012 American Physical Society
Version
Final published version
Abstract
The effect of [superscript 13]C isotope impurities on the phonon properties of graphene is discussed theoretically. We calculated the values of the phonon lifetimes due to isotope impurity scattering for all values of densities, isotopic masses, and for all wave vectors using second-order perturbation theory. We found that for natural concentrations of [superscript 13]C, the contribution of isotopic scattering to the phonon lifetime of the optical modes is negligible when compared to the electron-phonon interaction. Nevertheless, for atomic concentrations of [superscript 13]C as high as ρ=0.5 both contributions become comparable. Our results are compared with recent experimental results and we find good agreement both in the [superscript 13]C atomic density dependence of the lifetime as well as in the calculated spectral width of the G-band. Due to phonon scattering by [superscript 13]C isotopes, some graphene phonon wave functions become localized in real space. Numerical calculations show that phonon localized states exist in the high-energy optical phonon modes and in regions of flat phonon dispersion. In particular, for the case of in-plane optical phonon modes, a typical localization length is on the order of 3 nm for [superscript 13]C atomic concentrations of ρ≈0.5. Optical excitation of phonon modes may provide a way to experimentally observe localization effects for phonons in graphene.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.85.245406
