Chemistry Reference
In-Depth Information
(c) EDGE
(d) LO
(e) TO
(a) RBLM
(b) RBLM3
Fig. 5. Phonon eigenvectors of an
N
= 11 zigzag GNR for (a) RBLM, (b) RBLM3,
(c) Edge, (d) TO and (d) LO phonon modes.
58
It is important to note that the vibrational direction of the edge states
for the zigzag GNR is perpendicular to the zigzag edge direction, while that
for the armchair GNR is parallel to the armchair edge. It is a reason why TO
and EDGE has a similar polarization angle dependence in the case of zigzag
GNR. The edge phonon frequency of the zigzag edge is around 1430cm
−
1
,
which is consistent with previous calculations
44
and experiments.
36
We
can find a small intensities (not shown here) for two intermediate frequency
spectra show higher RBLM modes with five, and seven nodes whose angular
dependence is similar to RBLM.
4. Discussion and Summary
Separation of the LO and TO modes by changing the polarization directions
is interesting. Especially when these mode measure the electro-chemical
doping by applying a gate electrode, by which the Fermi energy can be
controlled, and the LO and TO phonon mode frequencies become soft due
to the Kohn anomaly effect.
45-56
Such Raman measurements for GNRs
will be important for identifying LO and TO phonon modes.
In the Raman measurements for GNRs, we expect the D band intensity
to be significant for armchair GNRs but not for zigzag GNRs. The present
calculation can not include the D band Raman spectra since the D band
is not a zone center phonon mode, but is rather a zone boundary phonon
mode with inter-valley elastic scattering occurring at the edge.
33,34
As is
