Controlling the Electronic Structure of Bilayer Graphene

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Science  18 Aug 2006:
Vol. 313, Issue 5789, pp. 951-954
DOI: 10.1126/science.1130681


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 led to control of the gap between valence and conduction bands. This control over the band structure suggests the potential application of bilayer graphene to switching functions in atomic-scale electronic devices.

Carbon-based materials such as carbon nanotubes (CNTs), graphite intercalation compounds, fullerenes, and ultrathin graphite films exhibit many exotic phenomena such as superconductivity (13) and an anomalous quantum Hall effect (46). These findings have caused renewed interest in the electronic structure of ultrathin layers of graphite, such as graphene: a single hexagonal carbon layer that 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 studied the valence band (VB) structure of a bilayer of graphene and demonstrated that through selective control of the carrier concentration in the graphene layers, one can easily tune the band structure near the Dirac crossing. Similar control can be achieved in 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 (79). 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 sp2 orbitals form a σ state with three neighboring carbon atoms, and one p orbital develops into delocalized π and π* states that form the highest occupied 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 ED, which at the normal half-filling condition coincides with the Fermi level (EF), resulting in a pointlike metallic Fermi surface (Fig. 2E).

Fig. 1.

Electronic structure of a single (A), symmetric double layer (B), and asymmetric double layer (C) of graphene. The energy bands depend only on in-plane momentum because the electrons are restricted to motion in a two-dimensional plane. The Dirac crossing points are at energy ED.

Fig. 2.

Energy-momentum dispersion relation of π, π*, and σ states of bilayer graphene. (A to C) Energy-momentum dispersion along high-symmetry directions. (D to F) Constant energy contours at EF, EF –0.4 eV = ED, and EF –2 eV. The high-symmetry points, directions, and BZ zone boundaries are indicated in (D).

Strictly speaking, undoped graphene is a semimetal because although there is a state crossing at ED = EF, the density of states there is zero and conduction is possible only with thermally excited electrons at finite temperature. In applying an effective mass description for the VB and CB (7), one arrives at a formal equivalence between the resulting differential equation and the Dirac equation, hence charge carriers in the vicinity of EF may be termed “Dirac fermions” (with the crossing point at K being named the Dirac point). Moreover, the particular band structure at the BZ boundary (that is, a linear dispersion) leads to an effective mass m* = 0 at the point where the VB and CB meet. The peculiar band structure in ultrathin graphite layers results in a number of unusual electronic transport properties, such as an anomalous quantum Hall effect (46, 10).

The graphene band structure is sensitive to the lattice symmetry. If the hexagonal layer structure is composed of nonequivalent elements, such as in boron nitride, the lateral, in-plane symmetry is broken, resulting in the 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). Because 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 EF 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 whether this gedanken experiment can be realized, we synthesized bilayer graphene films on a silicon carbide (SiC) substrate [6H polytype with (0001) orientation], following the recipe in (13), and measured their electronic properties using angle-resolved photoemission spectroscopy (ARPES) (14). As initially grown, our films had a slight n-type doping, acquired by depletion of the substrate's dopant carriers. Because we measured at low temperature, the dopant electrons in the SiC were frozen out and the substrate was a nearly perfect insulator, whereas the excess carriers left in the film, having been separated from their dopant atoms, had high mobility. Because the SiC states are well separated from both EF and ED [the SiC VB lies ∼2.6 eV below EF and the CB ∼0.4 eV above EF (15)], we can regard the bilayer graphene states as practically decoupled from the substrate and therefore as representing a true two-dimensional semimetal.

These films can sustain high current densities. At a temperature of 30 K, which is cold enough to preclude any conduction through the substrate, we can pass 400 mA through a macroscopic sample (5 by 15 mm), corresponding to a current of ∼1 nA (1010 to ∼1011 electrons/s) per graphene C atom, which is the same order of magnitude reported for single-walled 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 further n-type doping by the 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 ED (Fig. 1, B and 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 charge localization has been observed at the surface of graphite and graphene multilayers in an externally applied field (19, 20).

Figure 2, A to C, shows the binding energy–momentum dispersion relation of π, π*, and σ states along high-symmetry directions measured by ARPES. The ∼0.4-eV splitting of the π state (as in Fig. 1B) confirms that the sample is composed predominantly of two graphene layers (14). In Fig. 2, A and B, the crossing point ED can be clearly observed because this bilayer is n-type–doped through carrier depletion from the SiC substrate. In the constant-energy contours in the momentum space of π and π* states near EF (Fig. 2, D to F), we can clearly see the electron and hole pockets above and below ED, respectively. Besides the primary bilayer graphene states, we can identify six weak replicas of the π and π* states surrounding the primary states, especially in Fig. 2F. Low-energy electron diffraction shows that graphene layers grown on the SiC substrate display a nearly commensurate superstructure with relative lattice constant (Math) rotated 30° with respect to the substrate because of the difference between the graphene lattice constant of ∼2.46 Å and that of SiC, 3.07 Å (21). The replicas of the π and π* states are presumably brought about by scattering off of this superstructure in a fashion similar to those in other nearly incommensurate systems (22, 23).

The effects of doping the bilayers are shown in Fig. 3, which compares the as-prepared film (Fig. 3A) to two coverages of potassium. Our samples consisted predominantly of bilayer graphene, but depending on preparation conditions, we found minority regions of single- or triple-layer graphene within our probe area; the contribution of these minority domains has been subtracted from the data in Fig. 3. Beside the more or less rigid shift of the π and π* states toward higher binding energy because of an increased carrier concentration, the upper unoccupied π* state drops below EF at n = 0.0125 electron per unit cell (Fig. 3B) and continues dropping down with higher potassium coverage. The electron carrier densities of each stage are determined from the relative sizes of the Fermi surfaces with respect to the surface BZ of graphite.

Fig. 3.

Evolution of gap closing and reopening by changing the doping level by potassium adsorption. Experimental and theoretical bands (solid lines) (A) for an as-prepared graphene bilayer and (B and C) with progressive adsorption of potassium are shown. The number of doping electrons per unit cell, estimated from the relative size of the Fermi surface, is indicated at the top of each panel.

Plotted next to the intensity maps are calculated tight-binding bands (solid lines) (12), where the low-lying electronic states near the K point of the BZ are described by the solution of a simple 4 × 4 Hamiltonian as Math Math where the band index α = 1,2 and Math Math and Math.

Here k is the momentum in Å–1, ϕ is the azimuthal angle, v is the band velocity (m/s × ħ × 1010), U is the difference in the onsite Coulomb potentials of the two layers, γ1 (eV) and γ3 (eV) are out-of-plane nearest-neighbor and next–nearest-neighbor interaction parameters, and a (Å) is the graphite lattice constant (24, 25). These parameters are adjusted to reproduce the measured band structures over a large energy range (14). U is chosen to match the gap at the K point.

The most important feature in Fig. 3 is the variation in the apparent gap at the K point: first open in Fig. 3A, then closed in Fig. 3B, and finally open again in Fig. 3C. This gap variation is reproduced by our tight-binding calculation and is attributed to the variation in the relative potentials of the two layers as discussed above. Away from the K point, the gap is generally smaller than the prediction because the cusps extending into the gap between the π and π* bands are much sharper than in the model. As a result, the gap for the uncovered film (Fig. 3A) is not clearly resolved, although a shift of the bands is readily apparent from the flattening of the π* band edge and the lack of spectral weight at ED. Sufficient asymmetry was developed for higher doping that the gap is unambiguously open in Fig. 3C.

The measured π* state of bilayer graphene (Fig. 3C) does not agree with the tight-binding band, particularly around 200 meV below EF, where a slight kink is observed in the bands. This is presumably due to electron mass renormalization by electron-phonon coupling.

In order to systematically follow the evolution of the gap between π and π* states, photoemission spectra at the K point (the center cut of the bands in Fig. 3) as a function of doping are shown in Fig. 4A. The blue markers are the positions of the tight-binding π and π* bands. The data and calculated energies of the π and π* states clearly display the closing and reopening of the gap. The yellow line is the energy difference EFED, which increases by about 0.32 eV with respect to the as-grown sample, reflecting the overall doping level of the film.

Fig. 4.

Variation of states at the K point with increasing potassium coverage. (A) The image map shows the energy distribution curve at K as a function of potassium coverage. The blue markers are the fitted positions of the tight-binding π and π* bands, and the yellow line indicates ED. The closing and reopening of the gap between π and π* states are clearly shown. (B) The influence of doping concentration on the band parameters U and γ1.

The variation of carrier concentration has a marked influence on the band structure as derived from a comparison of the experimental results with the tight-binding calculation (Fig. 4). The Coulomb potential difference U displays a sign change at the electron concentration where the gap closes. It is expected that U increases with an increase of the charge difference in either graphene layer, induced by the fields at the respective interfaces. We have estimated the potential of each graphene layer from Poisson's equation, based on the Schottky barrier height of 0.4 eV (15), assuming infinitely thick graphene multilayers, and find that for the as-prepared sample, the potential difference between the first and second layers shows reasonable agreement with the Coulomb potential difference U estimated from the size of the gap evaluated in the tight-binding model. The resulting electric field in the graphene layers is similar in magnitude to that induced in a device structure (26). Moreover, a monotonic increase is seen in γ1, which measures the interlayer interaction as a function of electron concentration in both layers. This suggests that at higher electron density, the overlap between π orbitals of adjacent graphene layers increases. This may be due to the smaller interlayer distance caused by a shorter screening length.

Our results demonstrate that by controlling the carrier density in a bilayer of graphene, the occupation of electronic states near EF and the magnitude of the gap between the VB and CB can be manipulated. We have chosen potassium doping as a means of achieving this, but the switching functionality may be readily induced by an electric field across the bilayer in a device structure, in such a way that the potentials on either layer have opposite sign (10). The deposition of alkali atoms on epitaxially grown multilayer graphene films thus provides, beyond an opportunity to obtain their wave vector–resolved electronic structure as reported here, a path to studying their physical properties in a devicelike context.

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