Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy
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 perturbati...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/72164 https://orcid.org/0000-0001-8492-2261 https://orcid.org/0000-0002-3023-396X |
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| author | Rodriguez-Nieva, J. F. Saito, R. Costa, S. D. Dresselhaus, Mildred |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Rodriguez-Nieva, J. F. Saito, R. Costa, S. D. Dresselhaus, Mildred |
| author_sort | Rodriguez-Nieva, J. F. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:11:19Z |
| format | Article |
| id | mit-1721.1/72164 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:11:19Z |
| publishDate | 2012 |
| publisher | American Physical Society |
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| spelling | mit-1721.1/721642022-10-02T06:56:57Z Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy Rodriguez-Nieva, J. F. Saito, R. Costa, S. D. Dresselhaus, Mildred Massachusetts Institute of Technology. Department of Physics Dresselhaus, Mildred S. Rodriguez-Nieva, J. F. Dresselhaus, Mildred 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. National Science Foundation (U.S.). (Grant number DMR-10-1004147) 2012-08-15T20:39:33Z 2012-08-15T20:39:33Z 2012-06 2012-04 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/72164 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 https://orcid.org/0000-0001-8492-2261 https://orcid.org/0000-0002-3023-396X en_US http://dx.doi.org/10.1103/PhysRevB.85.245406 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Rodriguez-Nieva, J. F. Saito, R. Costa, S. D. Dresselhaus, Mildred Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy |
| title | Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy |
| title_full | Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy |
| title_fullStr | Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy |
| title_full_unstemmed | Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy |
| title_short | Effect of 13C isotope doping on the optical phonon modes in graphene: Localization and Raman spectroscopy |
| title_sort | effect of 13c isotope doping on the optical phonon modes in graphene localization and raman spectroscopy |
| url | http://hdl.handle.net/1721.1/72164 https://orcid.org/0000-0001-8492-2261 https://orcid.org/0000-0002-3023-396X |
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