tection efficiency for the read beam is $ ;
0.04, so we infer the efficiency of quantum
state transfer from the atoms onto the pho-
ton, O ; 0.03.
We have realized a quantum node by
combining the entanglement of atomic and
photonic qubits with the atom-photon quan-
tum state transfer. By implementing the
second node at a different location and
performing a joint detection of the signal
photons from the two nodes, the quantum
repeater protocol (11), as well as distant te-
leportation of an atomic qubit, may be real-
ized. Based on this work, we estimate the
rate for these protocols to be R
2
; ($O"n
s
)
2
R ;
3
10
j7
s
j1
. However, improvements in O
that are based on increasing the optical
thickness of atomic samples (16), as well as
elimination of transmission losses, could pro-
vide several orders of magnitude increase in
R
2
. Our results also demonstrate the possi-
bility of realizing quantum nodes consisting
of multiple atomic qubits by using multiple
beams of light. This approach shows prom-
ise for implementation of distributed quan-
tum computation (20, 21).
References and Notes
1. I. Chuang, M. Nielsen, Quantum Computation and
Quantum Information (Cambridge Univ. Press, Cam-
bridge, 2000).
2. S. Haroche, J. M. Raimond, M. Brune, in Experimental
Quantum Computation and Information,F.deMartini,
C. Monroe, Eds. (Proceedings of the International
School of Physics Enrico Fermi, course CXLVIII, IOS
Press, Amsterdam, 2002), pp. 37–66.
3. C. A. Sackett et al., Nature 404, 256 (2000).
4. M. D. Barrett et al., Nature 429, 737 (2004).
5. M. Riebe et al., Nature 429, 734 (2004).
6. B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe,
Nature 428, 153 (2004).
7. S. Bose, P. L. Knight, M. B. Plenio, V. Vedral, Phys. Rev.
Lett. 83, 5158 (1999).
8. H. J. Kimble, Phys. Scr. 76, 127 (1998).
9. A. Kuzmich, E. S. Polzik, in Quantum Information with
Continuous Variables, S. L. Braunstein, A. K. Pati, Eds.
(Kluwer, Dordrecht, 2003).
10. M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
11. L.-M. Duan, M. D. Lukin, I. J. Cirac, P. Zoller, Nature
414, 413 (2001).
12. A. Kuzmich et al., Nature 423, 731 (2003).
13. C. H. van der Wal et al., Science 301, 196 (2003).
14. W. Jiang, C. Han, P. Xue, L.-M. Duan, G. C. Guo, Phys.
Rev. A. 69, 043819 (2004).
15. C. W. Chou, S. V. Polyakov, A. Kuzmich, H. J. Kimble,
Phys. Rev. Lett. 92, 213601 (2004).
16. L.-M. Duan, J. I. Cirac, P. Zoller, Phys. Rev. A. 66,
023818 (2002).
17. A. Kuzmich, T. A. B. Kennedy, Phys. Rev. Lett. 92,
030407 (2004).
18. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev.
A. 60, 1888 (1994).
19. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K.
Wooters, Phys. Rev. A. 54, 3824 (1996).
20. Y. L. Lim, A. Beige, L. C. Kwek, www.arXiv.org/quant-ph/
0408043.
21. S. D. Barrett, P. Kok, www.arXiv.org/quant-ph/0408040.
22. We acknowledge fruitful conversations with T. A. B.
Kennedy, J. A. Sauer, L. You, A. Zangwill and, par-
ticularly, M. S. Chapman and thank R. Smith and E. T.
Neumann for experimental assistance. This work was
supported by NASA and the Research Corporation.
28 July 2004; accepted 16 September 2004
Electric Field Effect in Atomically
Thin Carbon Films
K. S. Novoselov,
1
A. K. Geim,
1
*
S. V. Morozov,
2
D. Jiang,
1
Y. Zhang,
1
S. V. Dubonos,
2
I. V. Grigorieva,
1
A. A. Firsov
2
We describe monocrystalline graphitic films, which are a few atoms thick but are
nonetheless stable under ambient conditions, metallic, and of remarkably high
quality. The films are found to be a two-dimensional semimetal with a tiny overlap
between valence and conductance bands, and they exhibit a strong ambipolar
electric field effect such that electrons and holes in concentrations up to 10
13
per
square centimeter and with room-temperature mobilities of È10,000 square
centimeters per volt-second can be induced by applying gate voltage.
The ability to control electronic properties of
a material by externally applied voltage is at
the heart of modern electronics. In many
cases, it is the electric field effect that allows
one to vary the carrier concentration in a
semiconductor device and, consequently,
change an electric current through it. As the
semiconductor industry is nearing the limits
of performance improvements for the current
technologies dominated by silicon, there is a
constant search for new, nontraditional mate-
rials whose properties can be controlled by
the electric field. The most notable recent
examples of such materials are organic
conductors (1) and carbon nanotubes (2). It
haslongbeentemptingtoextendtheuseof
the field effect to metals Ee.g., to develop all-
metallic transistors that could be scaled down
to much smaller sizes and would consume
less energy and operate at higher frequencies
than traditional semiconducting devices (3)^.
However, this would require atomically thin
metal films, because the electric field is
screened at extremely short distances (G1nm)
and bulk carrier concentrations in metals are
large compared to the surface charge that can
be induced by the field effect. Films so thin
tend to be thermodynamically unstable, be-
coming discontinuous at thicknesses of sev-
eral nanometers; so far, this has proved to be
an insurmountable obstacle to metallic elec-
tronics, and no metal or semimetal has been
shown to exhibit any notable (91%) field ef-
fect (4).
We report the observation of the electric
field effect in a naturally occurring two-
dimensional (2D) material referred to as
few-layer graphene (FLG). Graphene is the
name given to a single layer of carbon atoms
densely packed into a benzene-ring struc-
ture, and is widely used to describe proper-
ties of many carbon-based materials, including
graphite, large fullerenes, nanotubes, etc. (e.g.,
carbon nanotubes are usually thought of as
graphene sheets rolled up into nanometer-sized
cylinders) (5–7). Planar graphene itself has
been presumed not to exist in the free state,
being unstable with respect to the formation of
curved structures such as soot, fullerenes, and
nanotubes (5–14).
1
Department of Physics, University of Manchester,
Manchester M13 9PL, UK.
2
Institute for Microelec-
tronics Technology, 142432 Chernogolovka, Russia.
*To whom correspondence should be addressed.
E-mail: geim@man.ac.uk
R EPORTS
22 OCTOBER 2004 VOL 306 SCIENCE www.sciencemag.org666

We have been able to prepare graphitic
sheets of thicknesses down to a few atomic
layers (including single-layer graphene), to
fabricate devices from them, and to study
their electronic properties. Despite being
atomically thin, the films remain of high
quality, so that 2D electronic transport is
ballistic at submicrometer distances. No
other film of similar thickness is known to
be even poorly metallic or continuous under
ambient conditions. Using FLG, we demon-
strate a metallic field-effect transistor in
which the conducting channel can be
switched between 2D electron and hole gases
by changing the gate voltage.
Our graphene films were prepared by
mechanical exfoliation (repeated peeling) of
small mesas of highly oriented pyrolytic
graphite (15). This approach was found to
be highly reliable and allowed us to prepare
FLG films up to 10 6minsize.Thickerfilms
(d Q 3 nm) were up to 100 6m across and
visible by the naked eye. Figure 1 shows
examples of the prepared films, including
single-layer graphene Esee also (15)^.To
study their electronic properties, we pro-
cessed the films into multiterminal Hall bar
devices placed on top of an oxidized Si
substrate so that a gate voltage V
g
could be
applied. We have studied more than 60
devices with d G 10 nm. We focus on the
electronic properties of our thinnest (FLG)
devices, which contained just one, two, or
three atomic layers (15). All FLG devices
exhibited essentially identical electronic
properties characteristic for a 2D semimetal,
which differed from a more complex (2D
plus 3D) behavior observed for thicker,
multilayer graphene (15) as well as from
the properties of 3D graphite.
In FLG, the typical dependence of its sheet
resistivity D on gate voltage V
g
(Fig. 2)
exhibits a sharp peak to a value of several
kilohms and decays to È100 ohms at high V
g
(note that 2D resistivity is given in units of
ohms rather than ohms
cm as in the 3D
case). Its conductivity G 0 1/D increases
linearly with V
g
on both sides of the resistivity
peak (Fig. 2B). At the same V
g
where D has its
peak, the Hall coefficient R
H
exhibits a sharp
reversal of its sign (Fig. 2C). The observed
behavior resembles the ambipolar field effect
in semiconductors, but there is no zero-
conductanceregionassociatedwiththeFermi
level being pinned inside the band gap.
Our measurements can be explained
quantitatively by a model of a 2D metal
with a small overlap &( between conductance
and valence bands (15). The gate voltage
induces a surface charge density n 0 (
0
(V
g
/te
and, accordingly, shifts the position of the
Fermi energy (
F
. Here, (
0
and ( are the
permittivities of free space and SiO
2
, respec-
tively; e is the electron charge; and t is the
thickness of our SiO
2
layer (300 nm). For
typical V
g
0 100 V, the formula yields n ,
7.2
10
12
cm
j2
. The electric field doping
transforms the shallow-overlap semimetal
into either completely electron or completely
hole conductor through a mixed state where
both electrons and holes are present (Fig. 2).
The three regions of electric field doping are
clearly seen on both experimental and
theoretical curves. For the regions with only
electrons or holes left, R
H
decreases with
increasing carrier concentration in the usual
way, as 1/ne. The resistivity also follows the
standard dependence D
j1
0 G 0 ne6 (where
6 is carrier mobility). In the mixed state, G
changes little with V
g
, indicating the substi-
tution of one type of carrier with another,
while the Hall coefficient reverses its sign,
reflecting the fact that R
H
is proportional to
Fig. 1. Graphene films. (A) Photograph (in normal white light) of a relatively large multilayer
graphene flake with thickness È3 nm on top of an oxidized Si wafer. (B) Atomic force microscope
(AFM) image of 2 6mby26m area of this flake near its edge. Colors: dark brown, SiO
2
surface;
orange, 3 nm height above the SiO
2
surface. (C) AFM image of single-layer graphene. Colors: dark
brown, SiO
2
surface; brown-red (central area), 0.8 nm height; yellow-brown (bottom left), 1.2 nm;
orange (top left), 2.5 nm. Notice the folded part of the film near the bottom, which exhibits a
differential height of È0.4 nm. For details of AFM imaging of single-layer graphene, see (15). (D)
Scanning electron microscope image of one of our experimental devices prepared from FLG. (E)
Schematic view of the device in (D).
Fig. 2. Field effect in FLG. (A) Typical
dependences of FLG’s resistivity D on
gate voltage for different temperatures
(T 0 5, 70, and 300 K for top to bottom
curves, respectively). (B) Example of
changes in the film’s conductivity G 0
1/D(V
g
) obtained by inverting the 70 K
curve (dots). (C) Hall coefficient R
H
versus V
g
for the same film; T 0 5K.(D)
Temperature dependence of carrier
concentration n
0
in the mixed state
for the film in (A) (open circles), a
thicker FLG film (squares), and multi-
layer graphene (d , 5 nm; solid circles).
Red curves in (B) to (D) are the
dependences calculated from our mod-
el of a 2D semimetal illustrated by
insets in (C).
0
2
4
6
8
-100 -50 0 50 100
0
0.5
-100 0 100
0
3
100 300
2
4
6
D
C
B
ε
F
ρ
(
k
Ω
)
ε
F
A
δε
ε
F
R
H
(
k
Ω
T
/
)
V
g
(V)
V
g
(V)
σ (mΩ
-1
)
T (K)
n
0
(T )/n
0
(4K)
0
R EPORTS
www.sciencemag.org SCIENCE VOL 306 22 OCTOBER 2004 667