Absolute Raman matrix elements of graphene and graphite
Using sample substitution [Grimsditch et al., J. Raman Spectrosc. 10, 77 (1981)] we deconvolve the highly wavelength-dependent response of the spectrometer from the Raman spectra of graphene suspended on an SiO[subscript 2]-Si substrate and graphite for the D and G modes in the visible range. We der...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/60927 |
| _version_ | 1826214677197094912 |
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| author | Narula, Rohit Panknin, Robert Reich, Stephanie |
| author2 | Massachusetts Institute of Technology. Department of Materials Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Materials Science and Engineering Narula, Rohit Panknin, Robert Reich, Stephanie |
| author_sort | Narula, Rohit |
| collection | MIT |
| description | Using sample substitution [Grimsditch et al., J. Raman Spectrosc. 10, 77 (1981)] we deconvolve the highly wavelength-dependent response of the spectrometer from the Raman spectra of graphene suspended on an SiO[subscript 2]-Si substrate and graphite for the D and G modes in the visible range. We derive a model that considers graphene suspended on an arbitrary stratified medium while sidestepping its problematic ascription as an object of finite thickness and calculate the absolute Raman response of graphene (and graphite) via its explicitly frequency-independent Raman matrix element [Falicov and Martin, Light Scattering in Solids I: Introductory Concepts (Springer-Verlag, Berlin, 1983), p. 1083] |K2f,10′|[superscript 2] vs laser frequency. For both graphene and graphite the |K2f,10′|[superscript 2] per graphene layer vs laser frequency rises rapidly for the G mode and less so for the D mode over the visible range. Although we find a dispersion of the D mode position with laser frequency for both graphene and graphite of 41 cm[superscript −1]/eV and 35 cm[superscript −1]/eV, respectively, in good agreement with Narula and Reich [Phys. Rev. B 78, 165422 (2008)] assuming constant matrix elements, the observed intensity dependence is in disagreement. Finally, we show the sensitivity of our calculation to the variation in thickness of the underlying SiO[subscript 2] layer for graphene. Our findings shall serve as an experimental verification of the behavior of the relevant matrix elements in graphene and its allotropes that may be calculated theoretically in the future. |
| first_indexed | 2024-09-23T16:09:16Z |
| format | Article |
| id | mit-1721.1/60927 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:09:16Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/609272022-10-02T06:41:59Z Absolute Raman matrix elements of graphene and graphite Narula, Rohit Panknin, Robert Reich, Stephanie Massachusetts Institute of Technology. Department of Materials Science and Engineering Reich, Stephanie Reid, Stephanie Narula, Rohit Using sample substitution [Grimsditch et al., J. Raman Spectrosc. 10, 77 (1981)] we deconvolve the highly wavelength-dependent response of the spectrometer from the Raman spectra of graphene suspended on an SiO[subscript 2]-Si substrate and graphite for the D and G modes in the visible range. We derive a model that considers graphene suspended on an arbitrary stratified medium while sidestepping its problematic ascription as an object of finite thickness and calculate the absolute Raman response of graphene (and graphite) via its explicitly frequency-independent Raman matrix element [Falicov and Martin, Light Scattering in Solids I: Introductory Concepts (Springer-Verlag, Berlin, 1983), p. 1083] |K2f,10′|[superscript 2] vs laser frequency. For both graphene and graphite the |K2f,10′|[superscript 2] per graphene layer vs laser frequency rises rapidly for the G mode and less so for the D mode over the visible range. Although we find a dispersion of the D mode position with laser frequency for both graphene and graphite of 41 cm[superscript −1]/eV and 35 cm[superscript −1]/eV, respectively, in good agreement with Narula and Reich [Phys. Rev. B 78, 165422 (2008)] assuming constant matrix elements, the observed intensity dependence is in disagreement. Finally, we show the sensitivity of our calculation to the variation in thickness of the underlying SiO[subscript 2] layer for graphene. Our findings shall serve as an experimental verification of the behavior of the relevant matrix elements in graphene and its allotropes that may be calculated theoretically in the future. European Research Council (Grant No. 210642-OptNano) 2011-02-11T19:06:12Z 2011-02-11T19:06:12Z 2010-07 2010-06 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/60927 Narula, Rohit, Robert Panknin, and Stephanie Reich. “Absolute Raman matrix elements of graphene and graphite.” Physical Review B 82.4 (2010): 045418. © 2010 The American Physical Society. en_US http://dx.doi.org/10.1103/PhysRevB.82.045418 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 | Narula, Rohit Panknin, Robert Reich, Stephanie Absolute Raman matrix elements of graphene and graphite |
| title | Absolute Raman matrix elements of graphene and graphite |
| title_full | Absolute Raman matrix elements of graphene and graphite |
| title_fullStr | Absolute Raman matrix elements of graphene and graphite |
| title_full_unstemmed | Absolute Raman matrix elements of graphene and graphite |
| title_short | Absolute Raman matrix elements of graphene and graphite |
| title_sort | absolute raman matrix elements of graphene and graphite |
| url | http://hdl.handle.net/1721.1/60927 |
| work_keys_str_mv | AT narularohit absoluteramanmatrixelementsofgrapheneandgraphite AT pankninrobert absoluteramanmatrixelementsofgrapheneandgraphite AT reichstephanie absoluteramanmatrixelementsofgrapheneandgraphite |