Chemistry Reference
In-Depth Information
is quadratic already for the MLG, as a consequence of the screening of the collective
mode by the metal substrate. The screening in MLG on metal substrates is clearly
more effective with respect to the case of graphene layers grown on the semiconduc-
tor silicon carbide substrate. This should explain the quadratic dispersion recorded
in MLG/Ni(111) (Ref. Generalov and Dedkov
2012
) and MLG/Pt(111) (our data), in
spite of the very different band structure of such two graphene/metal interfaces. We
also remind that the plasmon dispersion in the long-wavelength limit is predicted to
be quadratic with respect to momentum for the interacting electron gas (Pines
1964
).
Another issue to be considered is the interlayer coupling. Concerning supported
graphene, the interlayer interaction varies as a function of the electron density in
the layers. At higher electron density the overlap between orbitals of adjacent layers
increases, thus increasing the interlayer coupling (López-Sancho et al.
2007
). Hence,
in principle the fact that MLG is hole-doped by charge transfer from the Pt substrate
(Fermi level below Dirac point) (Gao et al.
2010
) could influence the electronic
response of the interface. As regards graphite, it is worth mentioning that its interlayer
coupling is still under debate. Band structure calculations predicted an interlayer
coupling much larger than the values deduced by c-axis conductivity measurements
(Dion et al.
2004
; Nilsson et al.
2006
).
A key factor in the propagation of the plasmonic excitation is its lifetime, which
is limited by the decay into electron-hole pairs (Landau damping) (Yuan and Gao
2008
). The damping of the plasmon peak is clearly revealed by the trend of the
FWHM versus
q
||
, reported in Fig.
3.23
. The width of the plasmon rapidly increases
with
q
||
due to the occurrence of Landau damping. It is worth remembering that, in
contrast with the low-energy sheet plasmon (Politano et al.
2011d
; Langer et al.
2010
), the
-plasmon is a mode which lies inside the continuum of particle-hole
excitations and therefore it will be damped even at
q
||
→
π
0 (Yuan et al.
2011
).
plasmon in MLG/6H-SiC(0001) initially
decreased up to 0.1 Å
−
1
, followed by a steep increase as a function of
q
||
. A simi-
lar behaviour has been recorded on graphite (Papageorgiou et al.
2000
), where the
turning point has been found at 0.3-0.4 Å
−
1
. The absence of a turning point in
MLG/Pt(111) could be related to the nearly-linear dispersion of
On the other hand, the width of the
π
bands in the Dirac
cones (Sutter et al.
2009
). Instead, substrate interactions in graphene on silicon car-
bide are known to distort the linear dispersion near the Dirac point in the first graphene
layer (Zhou et al.
2007
). They cause the appearance of a 260 meV energy gap and
enhanced electron-phonon coupling (Zhou et al.
2007
). This gap decreases as the
sample thickness increases and eventually approaches zero for multilayer graphene.
The behavior of the FWHM as a function of the plasmon energy (Fig.
3.23
b) showed
that for MLG/Pt(111) there is an enhanced broadening of the plasmon peak around
6.3 eV. These findings indicate that the Landau damping processes of the
π
π
plasmon
in MLG/Pt(111) are mainly due to
* interband transitions centered around 6.3 eV.
By comparing the FWHM in the long wave-length limit for various graphene sys-
tems (Table
3.1
), it is quite evident that the presence of out-of-plane decay channels
reflects into a wider line-width of the plasmon peak, i.e. a shorter lifetime of the
plasmon mode. As demonstrated for graphite (Marinopoulos et al.
2004
), they cause
additional damping of plasmons, which result in a more diffuse shape for the loss
π
-
π
