The authors model the optical visibility of monolayer and bilayer graphene deposited on a SiO2Si substrate or thermally annealed on the surface of SiC. Visibility is much stonger in reflection than in transmission, reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.

1.
K. S.
Novoselov
,
A. K.
Geim
,
S. V.
Morozov
,
D.
Jiang
,
Y.
Zhang
,
S. V.
Dubonos
,
I. V.
Grigorieva
, and
A. A.
Firsov
,
Science
306
,
666
(
2004
).
2.
K. S.
Novoselov
,
A. K.
Geim
,
S. V.
Morozov
,
D.
Jiang
,
M. I.
Katsnelson
,
I. V.
Grigorieva
, and
S. V.
Dubonos
,
Nature (London)
438
,
197
(
2005
).
3.
Y.
Zhang
,
J. P.
Small
,
M. E. S.
Amori
, and
P.
Kim
,
Phys. Rev. Lett.
94
,
176803
(
2005
);
[PubMed]
Y.
Zhang
,
Y.
Tan
,
H. L.
Stormer
, and
P.
Kim
,
Nature (London)
438
,
201
(
2005
).
4.
A.
Geim
and
K.
Novoselov
,
Nat. Mater.
6
,
183
(
2007
).
5.
R.
Saito
,
G.
Dresselhaus
and
M. S.
Dresselhaus
,
Physical Properties of Carbon Nanotubes
(
Imperial College
,
London
,
1998
),
28
;
T.
Ando
,
J. Phys. Soc. Jpn.
74
,
777
(
2005
).
6.
E.
McCann
and
V. I.
Fal’ko
,
Phys. Rev. Lett.
96
,
086805
(
2006
).
7.
K. S.
Novoselov
,
E.
McCann
,
S. V.
Morozov
,
V. I.
Fal’ko
,
M. I.
Katsnelson
,
U.
Zeitler
,
D.
Jiang
,
F.
Schedin
, and
A. K.
Geim
,
Nat. Phys.
2
,
177
(
2006
).
8.
T.
Ohta
,
A.
Bostwick
,
T.
Seyller
,
K.
Horn
, and
E.
Rotenberg
,
Science
313
,
951
(
2006
);
[PubMed]
A.
Bostwick
,
T.
Ohta
,
T.
Seyller
,
K.
Horn
, and
E.
Rotenberg
,
Nat. Phys.
3
,
36
(
2007
).
9.

We take data for the real and imaginary parts of the permittivity of Si from Ref. 10. The imaginary part is substantial only for ω>1.5eV, so we approximate ImϵSi(ω<1.5eV)0. The permittivity of SiO2 is nearly dispersionless in this frequency range (Ref. 11), so we take the SiO2 dielectric constant as εSiO2=3.9. SiC has some dispersion for these frequencies12 but the imaginary part is negligible so we assume ImϵSiC(ω)0.

10.
J.
Leng
,
J.
Opsal
,
H.
Chu
,
M.
Senko
, and
D. E.
Aspnes
,
Thin Solid Films
313-314
,
132
(
1998
).
11.
H. F.
Wolf
,
Silicon Semiconductor Data
(
Pergamon
,
Oxford
,
1969
),
602ff
.
12.
M.
Kildemo
,
Thin Solid Films
455-456
,
187
(
2004
).
13.
L. A.
Falkovsky
and
A. A.
Varlamov
, e-print arXiv:cond-mat/0606800.
14.
J.
Nilsson
,
A. H.
Castro Neto
,
F.
Guinea
, and
N. M. R.
Peres
,
Phys. Rev. Lett.
97
,
266801
(
2007
).
15.
D. S. L.
Abergel
and
V. I.
Fal’ko
,
Phys. Rev. B
75
,
155430
(
2007
).
16.
P.
Blake
,
E. W.
Hill
,
A. H.
Castro Neto
,
K. S.
Novoselov
,
D.
Jiang
,
R.
Yang
,
T. J.
Booth
, and
A. K.
Geim
,
Appl. Phys. Lett.
91
,
063124
(
2007
).
17.
C.
Berger
,
Z.
Song
,
T.
Li
,
X.
Li
,
A. Y.
Ogbazghi
,
R.
Feng
,
Z.
Dai
,
A. N.
Marchenkov
,
E. H.
Conrad
,
P. N.
First
, and
W. A.
de Heer
,
J. Phys. Chem. B
108
,
19912
(
2004
).
You do not currently have access to this content.