Raman Spectroscopy of Graphene Edges - Graphene and Its Fascinating Attributes - page 99

discussed in the Introduction, inter-valley elastic scattering occurs only at
the armchair edge, while intra-valley elastic scattering occurs at the zigzag
edge. 30-32 Raman imaging of the D band of graphite shows that the D-band
intensity is strong about 20nm away from the edge. 32 Thus the D band
of armchair GNRs is strong relative to the G-band intensity, especially for
small width GNRs of around 20nm and smaller. The width dependence of
the D band is another point that should be addressed by future experiments.
In the previous first principles calculations, 36,44 the C-C bond at the
armchair edge becomes a triple bond, because the dangling bonds of the
two carbon atoms at the edge make an additional bond at the edges.

The corresponding vibration frequency then becomes 2010cm − 1 which is
similar to the frequency of polyene in SWNTs. 57 In the present calculation,
however, the change of the force constants at the edge is not included and
thus the corresponding frequency appears at a much lower value. In the
experiment, the dangling bonds are terminated by H atoms and form sp 2
covalent bonds. In this case, the frequency of the vibration is observed at
1530cm − 1 . 36 Thus special care is needed in the case of a comparison with
experiment if we uses the current force constant sets for graphene ribbon
are used.
In summary, we have calculated the Raman intensity for an armchair
and zigzag GNR within non-resonance bond polarization theory. Depend-
ing on the polarization direction, LO, TO, RBLM, and EDGE Raman-
active phonon modes can be selected. Especially, the LO and TO modes
show an opposite polarization dependence for their intensities and for the
vibration direction for armchair and zigzag GNRs. The edge phonon vi-
bration direction is parallel and perpendicular to the edge for armchair and
zigzag GNRs, respectively. Such a behavior is therefore useful for deter-
mining the edge identification for these edges using Raman spectroscopy.

π

Acknowledgments

RS acknowledges Mr. Masaru Furukawa, Professor Mildred S. Dresselhaus
and Dr. Ken'ichi Sasaki for valuable discussion for making this article.
This work is supported by MEXT grant (No. 20241023) Japan.

References

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Grigorieva, I. V., Dubonus, S. V. and Firsov, A. A., Two-dimensional gas of
massless Dirac fermions in graphene, Nature , 438:197, 2005.