Dirac Fermions in Graphene and Graphite—a view from angle ...

in Fig. 5.2(a) for example). Finally, we wish to attempt to estimate the amount of NO 2 adsorbed on the
graphene. The amount of carrier concentration has been estimated by measuring the area enclosed by the
Fermi contours and through the Luttinger theorem. From panel a to panel b we detected a change of carrier
concentration by 0.0052 electrons per unit cell (4 carbon atoms) upon exposing the graphene sample to 0.6L
of NO 2 . Transport measurements suggested that as much as 1 electron is transferred to each molecule of
NO 2 adsorbed 89 . If we take this estimate, change of 0.0052 electrons per unit cell corresponds to 0.033
Langmuir of NO 2 . This suggests that with the dosage 0.6L NO 2 molecules, only 5.5% of the molecules stick
to graphene and remove 1 electron from graphene. This is reasonable considering the fast photodesorption
of the NO 2 molecules.
5.4 Metal-insulator transition in single layer graphene
In Figure 5.3 we show the effect of molecular doping on single layer epitaxial graphene for various
amounts of NO 2 doping. Data in panel a are taken on the as-grown sample, which is electron doped with
the Dirac point located at 0.4 eV below E F . The dispersion near the Dirac point shows deviations from the
expected conical dispersion as previously reported 63,71 . The origin of these deviations has been a matter
of intense debate in the past year and has been attributed either to a kink structure caused by electronplasmon
interaction 71 or to the opening of a gap at the K point 63 . By hole doping we have the unique ability
to directly access this region and to investigate its origin. Panels b-f show data taken for the progressive
adsorption of NO 2 on a single layer graphene sample. Similar to the case of bilayer graphene, we can dope
the single layer sample and move the chemical potential from the conduction band all the way down to the
valence band. The maximum shift of 0.8 eV corresponds to a gate voltage as large as 300 V in the case of the
exfoliated graphene 5,52 . When the chemical potential falls in the anomalous region near E D (panels c and
d), extrapolation of the valence band shows that it lies below E F , while the conduction band is above E F .
Therefore a semiconducting graphene is achieved. To further support this, in panel g we show the EDCs
at the K point where peaks are closest to E F . When the chemical potential falls within the conduction or
valence bands (curves a, b, e, f), a peak near E F (dotted line) can be observed, while when the chemical
potential falls within the anomalous region near E D (curves c, d), a depletion of the spectral weight near E F
and a shift of the leading edge toward higher binding energy is evident. The results shown here demonstrate
that a metal to insulator to metal transition can be induced in hole doped epitaxial graphene. These results
further supports that the origin of the anomalous region in the dispersion near the Dirac point energy is due
to a gap 63 and not to many body interactions 71 . As previously pointed out 63 , a peculiar feature of the gap
is the non-zero intensity inside the gap region. The source of such spectral weight may be due to edge states
associated with the terrace or defect states 69 .
Figure 5.4 summarizes the effect of hole doping in single layer graphene. Rigid shift of the overall band
structure, which appears to take place upon doping, offers an easy way of estimating the amount of doping.
Figure 5.4(a) shows the shift of the Dirac point energy by increasing the charge carrier concentration through
molecular doping. For the as-grown single layer graphene (Fig. 5.3(a)), the separation of the Fermi wave
vectors is 0.096 Å −1 . Assuming that the electron pocket at E F is a circle, this converts to an electron
concentration of 1.4×10 13 cm −2 . For the highest doping achieved the distance between the Fermi vectors is
0.125 Å −1 which corresponds to a hole concentration of 2.4×10 13 cm −2 . Figure 5.4(b) plots the Fermi velocity
v F , a quantity that governs the low-energy quasiparticle dynamics, as a function of carrier concentration. v F
is extracted from the slope of the dispersion near E F , v= 1
. Surprisingly we find that the Fermi velocity
is nearly constant for all doping to within ±20% of the initial value, though small changes expected on a
scale which is beyond the resolution of the present experiment 94 cannot be excluded. This independence
of the Fermi velocity is different from the earlier report of a huge change of the Fermi velocity by electron
doping through Ca 67 in epitaxial graphene. Whether this suggests the presence of a strong electron-hole
asymmetry or the hybridization of the Ca band with the C π band 70 has to be confirmed. Finally, we
note that a similar doping independent Fermi velocity has been reported for the nodal quasiparticles in
high temperature superconductors, which are also Dirac fermions, through the insulator to superconducting
∂E
∂k
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