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Controlling the Electronic Structure of Bilayer Graphene
Taisuke Ohta,
1,2
*
Aaron Bostwick,
1
*
Thomas Seyller,
3
Karsten Horn,
2
Eli Rotenberg
1**
1
Advanced Light Source, E. O. Lawrence Berkeley National Laboratory, USA
2
Department of Molecular Physics, Fritz Haber Institute, Germany
3
Institut für Physik der Kondensierten Materie, Universität Erlangen-Nürnberg, Germany
* Contributed equally to this work
** To whom correspondence should be addressed
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We describe the synthesis of bilayer graphene thin films deposited on
insulating silicon carbide and report the characterization of their electronic
band structure using angle-resolved photoemission. By selectively
adjusting the carrier concentration in each layer, changes in the Coulomb
potential lead to a control of the gap between valence and conduction
bands. This control over the band structure suggests potential application
of bilayer graphene to switching functions in atomic-scale electronic
devices.
Carbon-based materials such as carbon nanotubes (CNTs), graphite intercalation
compounds (GICs), fullerenes, and ultrathin graphite films exhibit many exotic
phenomena such as superconductivity (1,2,3) and anomalous quantum Hall effect (4,5,6).
These findings have caused a renewed interest in the electronic structure of ultrathin
layers of graphite, such as graphene, a single hexagonal carbon layer which is the
building block for these materials. There is a strong motivation to incorporate graphene
multilayers into atomic-scale devices, spurred on by rapid progress in their fabrication
and manipulation.
We study the valence band structure of a bilayer of graphene, and demonstrate that
through selective control of carrier concentration in the graphene layers, one can easily
tune the band structure near the Dirac crossing. Similar control can be achieved in
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principle by varying the electric field across the bilayer film in an atomic-scale switching
device.
The electronic states of graphene can be well-described within basic calculational
schemes (7,8,9). Graphene is a flat layer of carbon atoms arranged in a hexagonal lattice
with two carbon atoms per unit cell. Of the four valence states, three sp
2
orbitals form a
σ state with three neighboring carbon atoms, while one p orbital develops into
delocalized π and π* states which form the highest occupied valence band (VB) and the
lowest unoccupied conduction band (CB). The π and π* states of graphene are degenerate
at the corner (K point) of the hexagonal Brillouin zone (BZ) (Fig. 1A). This degeneracy
occurs at the so-called Dirac crossing energy E
D
, which at the normal half-filling
condition coincides with the Fermi level (E
F
) resulting in a point-like metallic Fermi
surface (see Fig. 2E).
Strictly speaking, undoped graphene is a semimetal because although there is a state
crossing at E
D
=E
F
, the density of states there is zero and conduction is only possible with
thermally excited electrons at finite temperature. In applying an effective mass
description for the valence and conduction bands, (7) one arrives at a formal equivalence
between the resulting differential equation and the Dirac equation, hence charge carriers
in the vicinity of the Fermi level E
F
may be termed “Dirac Fermions” (with the crossing
point at K being named the “Dirac point”). Moreover, the particular band structure at the
Brillouin zone boundary, i.e. a linear dispersion, leads to an effective mass m* = 0 at the
point where valence and conduction bands meet. The peculiar band structure in ultrathin
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graphite layers results in a number of unusual electronic transport properties, such as an
anomalous quantum Hall effect (4,5,6,10).
The graphene band structure is sensitive to the lattice symmetry. If the hexagonal layer
structure is composed of non-equivalent elements, such as in boron nitride, the lateral, in-
plane symmetry is broken, resulting in formation of a large gap between π and π* states
(11). The symmetry can also be broken with respect to the c-axis by stacking two
graphene layers in Bernal stacking (the stacking fashion of graphite) as suggested by
McCann and Fal’ko (12) (Fig. 1B). Since the unit cell of a bilayer contains four atoms,
its band structure acquires two additional bands, π and π* states, in each valley split by
interlayer (A-B) coupling, and two lower-energy bands. If the individual graphene layers
in a bilayer are rendered inequivalent (Fig. 1C), then, an energy gap between low-energy
bands forms at the former Dirac crossing point (12). Provided that the charge state is
such that the Fermi level lies within the gap, a semimetal-to-insulator transition occurs. If
this symmetry breaking could be controlled externally, the electronic conductivity would
change through this transition, suggesting that a switch with a thickness of two atomic
layers could be constructed.
To see if this gedanken experiment can be realized, we have synthesized bilayer
graphene films on a silicon carbide substrate (6H polytype with (0001) orientation),
following the recipe in ref 13, and have measured their electronic properties using angle
resolved photoemission spectroscopy (ARPES) 14. As initially grown, our films have a
slight n-type doping, acquired by depletion of the substrate’s dopant carriers. Because
we measure at low temperature, the dopant electrons in the silicon carbide are frozen out
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and the substrate is a nearly perfect insulator, while the excess carriers left in the film,
having been separated from their dopant atoms, have a high mobility. As the SiC states
are well-separated from both E
F
and E
D
(the SiC valence band lies ~2.6 eV below E
F
, and
the conduction band ~0.4 eV above E
F
(15)), we can regard the bilayer graphene states as
practically decoupled from the substrate and therefore as representing a true two-
dimensional semi-metal.
These films can sustain high current densities. At 30K temperature, cold enough to
preclude any conduction through the substrate, we can pass 400 mA through a
macroscopic sample (5 × 15 mm), corresponding to a current of ~1 nA (10
10
~10
11
electrons per second) per graphene C atom, the same order of magnitude reported for
single wall CNTs (16) and graphene multilayers (10).
The symmetry of the bilayers is broken by the dipole field created between the
depletion layer of the SiC and the accumulation of charge on the graphene layer next to
the interface, rendering the two graphene layers inequivalent with respect to charge and
electrostatic potential in the as-prepared films. We can induce a further n-type doping by
deposition of potassium atoms onto the vacuum side, which donate their lone valence
electrons to the surface layer, forming another dipole (17,18). These surface and
interface dipole fields together act as the symmetry-breaking factor which controls the
presence or absence of the gap at the crossing energy E
D
(Figs. 1B-C). The net dipole
field between the two graphene layers results from the short screening length (~4 Å)
along the c-axis (7) which is comparable to the layer thickness (~3.4 Å). A similar
