Optical conductance and transmission in bilayer graphene
H. M. Dong, J. Zhang, F. M. Peeters, and W. Xu
Citation: J. Appl. Phys. 106, 043103 (2009); doi: 10.1063/1.3200959
View online: /10.1063/1.3200959
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Published by the American Institute of Physics.
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Optical conductance and transmission in bilayer graphene
H.M.Dong,1J.Zhang,2F.M.Peeters,3and W.Xu1,2,a͒
1Key Laboratory of Materials Physics,Institute of Solid State Physics,Chinese Academy of Sciences,
Hefei230031,China
2Department of Physics,Yunnan University,Kunming610015,China
3Department of Physics,University of Antwerp,Groenenborgerlaan171,B-2020Antwerpen,Belgium
͑Received5May2009;accepted10July2009;published online20August2009͒
We present a theoretical study of the optoelectronic properties of bilayer graphene.The optical conductance and transmission coefficient are calculated using the energy-balance equation derived from a Boltzmann equation for an air/graphene/dielectric-wafer system.For short wavelengths͑Ͻ0.2m͒,we obtain the universal optical conductance=e2/͑2ប͒.Interestingly,there exists an optical absorption window in the wavelength range10–100m,which is induced by different transition energies required for inter-and intra-band optical absorptions in the presence of the Moss–Burstein effect.As a result,the position and width of this absorption window depend sensitively on temperature,carrier density,and sample mobility of the system.These results are relevant for applications of recently developed graphene devices in advanced optoelectronics such as the infrared photodetectors.©2009American Institute of Physics.͓DOI:10.1063/1.3200959͔
I.INTRODUCTION
Graphene is the basis of a new class of nanostructures
where conduction occurs in single or few layers of carbon
atoms arranged in a hexagonal lattice.1Owing to its unique
electronic band structure and the corresponding quasirelativ-
istic features,graphene has attracted a great attention in re-
cent years.Furthermore,graphene can have a high carrier
density and exhibits high electronic mobility even at room
temperature.One of the major advantages of a graphene de-
vice is that the carrier density in the graphene layer can be
controlled very effectively through a gate voltage.1Hence,
graphene has been proposed as a“building block”for ad-
vanced electronic devices2such as graphene p-n and p-n-p
junctions,3transistors,4etc.In recent years,the study of the
electronic transport properties of Dirac quasiparticles in
graphene has rapidly become an important research topic in
nanomaterial science,condensed matter physics,and
nanoelectronics,5which is partly motivated by the possible
applications of graphene in advanced electronic devices.6
Recently,the optical and optoelectronic properties of dif-
ferent graphene systems have been investigated.In particu-
lar,it was found experimentally that the optical conductance
per graphene layer is given by a universal value=e2/͑4ប͒in the visible frequency and UV range.7As a con-sequence,the light transmittance of monolayer and bilayer
graphene devices are about0.98and0.96,respectively,in the
visible bandwidth.8This important discovery has resulted in
the proposal that graphene can be used to replace conven-
tional indium tin oxide electrodes for making better and
cheaper optical displays.9Kuzmenko et al.7recently found
experimentally that for photon energy smaller than0.2eV,
there is an optical absorption window.The width and depth
of this window depend strongly on temperature.This inter-
estingfinding implies that graphene may also be applied for infrared detection in ambient condition.Very recent experi-
mental work showed that graphene can have strong intra-
and inter-band transitions which can be substantially modi-
fied through electrical gating,similar to resistance tuning in
graphenefield-effect transistors.10These experimental results
show clearly that graphene can be used not only as advanced
electronic devices but also as optical devices for various ap-
plications.
In conjunction with experimental investigations into op-
toelectronic properties of graphene systems,theoretical study
in this area has been quite active.The universal optical con-
ductance in the visible regime,0=e2/4បper graphene layer, has been obtained theoretically.7,11The features of graphene
systems under far-infrared͑FIR͒or terahertz radiation have
also been investigated theoretically using various
approaches.12,13The results obtained from these theoretical
investigations have indicated that͑i͒in the short wavelength
such as visible regime,inter-band transition is the principal
channel for optical absorption and conductance in
graphene;7,11͑ii͒in the FIR or terahertz bandwidth,both inter-and intra-band transitions play important roles to cause optical absorption and conductance in graphene;12,13and͑iii͒the optoelectronic properties for graphene in the FIR or tera-hertz regime depend strongly on temperature and carrier den-sity in the system.12
The optical and optoelectronic properties of monolayer
graphene has been well documented.7,8,10In contrast to a
nearly linear energy spectrum in monolayer graphene,bi-
layer graphene has a quadratic energy spectrum in low en-
ergy regime.14,15Thus,the density of states in a bilayer
graphene system differs significantly from that in monolayer
graphene.It has been realized that bilayer graphene is of
equal importance as monolayer graphene for both techno-
logical applications and fundamental science.4,16In this pa-
per we present a detailed theoretical study of the optoelec-
tronic properties of bilayer graphene.In Sec.II,the
theoretical approach is developed to calculate the optoelec-
a͒Electronic mail:wenxu_issp@.
JOURNAL OF APPLIED PHYSICS106,043103͑2009͒
0021-8979/2009/106͑4͒/043103/6/$25.00©2009American Institute of Physics
106,043103-1
