The authors proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation. The Gruneisen parameters were introduced separately for the longitudinal and transverse phonon branches through averaging over phonon modes obtained from the first principles. The calculations show that Umklapp-limited thermal conductivity of graphene grows with the increasing linear dimensions of graphene flakes and can exceed that of the basal planes of bulk graphite when the flake size is on the order of a few micrometers. The obtained results are in agreement with experimental data and reflect the two-dimensional nature of phonon transport in graphene.

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
);
[PubMed]
K. S.
Novoselov
,
A. K.
Geim
,
S. V.
Morozov
,
D.
Jiang
,
M. I.
Katsnelson
,
I. V.
Grigorieva
,
S. V.
Dubonos
, and
A. A.
Firsov
,
Nature (London)
438
,
197
(
2005
);
A. K.
Geim
and
K. S.
Novoselov
,
Nature Mater.
6
,
183
(
2007
).
2.
Y. B.
Zhang
,
Y. W.
Tan
,
H. L.
Stormer
, and
P.
Kim
,
Nature (London)
438
,
201
(
2005
).
3.
A. A.
Balandin
,
S.
Ghosh
,
W.
Bao
,
I.
Calizo
,
D.
Teweldebrhan
,
F.
Miao
, and
C. N.
Lau
,
Nano Lett.
8
,
902
(
2008
).
4.
S.
Ghosh
,
I.
Calizo
,
D.
Teweldebrhan
,
E. P.
Pokatilov
,
D. L.
Nika
,
A. A.
Balandin
,
W.
Bao
,
F.
Miao
, and
C. N.
Lau
,
Appl. Phys. Lett.
92
,
151911
(
2008
).
5.
I.
Calizo
,
A. A.
Balandin
,
W.
Bao
,
F.
Miao
, and
C. N.
Lau
,
Nano Lett.
7
,
2645
(
2007
);
[PubMed]
I.
Calizo
,
F.
Miao
,
W.
Bao
,
C. N.
Lau
, and
A. A.
Balandin
,
Appl. Phys. Lett.
91
,
071913
(
2007
).
6.
A. A.
Balandin
,
S.
Ghosh
,
D.
Teweldebrhan
,
I.
Calizo
,
D. L.
Nika
, and
E. P.
Pokatilov
,
Proceedings of International Symposium on Graphene Devices
, Aizu-Wakamatsu, Japan,
2008
(unpublished), pp.
22
23
.
7.
D. L.
Nika
,
E. P.
Pokatilov
,
A. S.
Askerov
, and
A. A.
Balandin
,
Phys. Rev. B
79
,
155413
(
2009
).
8.
J. W.
Jiang
,
J. S.
Wang
, and
B.
Li
, arXiv:0902.1836v1.
9.
P. G.
Klemens
,
J. Wide Bandgap Mater.
7
,
332
(
2000
).
10.
P. G.
Klemens
,
Int. J. Thermophys.
22
,
265
(
2001
).
11.
N.
Mounet
and
N.
Marzari
,
Phys. Rev. B
71
,
205214
(
2005
).
12.
C. Y.
Ho
,
R. W.
Powell
and
P. E.
Liley
,
J. Phys. Chem. Ref. Data
3
,
1
(
1974
).
13.
L.
Braginsky
,
V.
Shklover
,
H.
Hofmann
, and
P.
Bowen
,
Phys. Rev. B
70
,
134201
(
2004
).
14.
M.
Shamsa
,
W. L.
Liu
,
A. A.
Balandin
, and
J. L.
Liu
,
Appl. Phys. Lett.
87
,
202105
(
2005
);
W. L.
Wu
,
M.
Shamsa
,
I.
Calizo
,
A. A.
Balandin
,
V.
Ralchenko
,
A.
Popovich
, and
A.
Saveliev
,
Appl. Phys. Lett.
89
,
171915
(
2006
);
M.
Shamsa
,
S.
Ghosh
,
I.
Calizo
,
V.
Ralchenko
,
A.
Popovich
, and
A. A.
Balandin
,
J. Appl. Phys.
103
,
083538
(
2008
).
15.
S.
Subrina
and
D.
Kotchetkov
,
J. Nanoelectron. Optoelectron.
3
,
249
(
2008
).
16.
G.
Ko
and
J.
Kim
,
Electrochem. Solid-State Lett.
12
,
H29
(
2009
).
17.
Q.
Shao
,
G.
Liu
,
D.
Teweldebrhan
, and
A. A.
Balandin
,
Appl. Phys. Lett.
92
,
202108
(
2008
).
18.
J.
Lan
,
J.-S.
Wang
,
C. K.
Gan
, and
S. K.
Chin
,
Phys. Rev. B
79
,
115401
(
2009
).
You do not currently have access to this content.