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

Figure 4.2. Observation of the gap opening in single layer graphene at the K point. (a) Structure
of graphene in the real and momentum space. (b) ARPES intensity map taken along the black line
in the inset of panel (a). The dispersions (black lines) are extracted from the EDC peak positions
shown in panel (c). (c) EDCs taken near the K point from k 0 to k 12 as indicated at the bottom of
panel (b). (d) MDCs from E F to -0.8 eV. The blue lines are inside the gap region, where the peaks
are non-dispersive. (e) Angle integrated intensity, which shows a suppression of intensity near E D .
a gap of approximately 0.26 eV. Another way of extracting the gap is from the MDC peaks. As already
discussed in Chapter 2 (section 2.1.4), MDCs are non-dispersive inside the gap region. The MDC peaks are
non-dispersive within the same energy window, 0.26 eV around E D (blue lines in panel d).Clearly away from
this region, the MDC peaks start dispersing again, in agreement with a conical dispersion. Another signature
of the gap opening is that the angle integrated intensity, which is proportional to the density of states (DOS)
integrated over one dimension, shows a suppression near the same region around E D (see Fig. 4.2(e)). This
suppression of intensity is typical of a gap opening.
A peculiar feature of this gap is that there is non-zero intensity around E D (panel b) between the valence
and conduction bands. The direct comparison with a cut away from the K point, where a gap is certainly
present due to the conical dispersion (see Fig. 4.3 and Fig. 4.4(c)) suggests that this non-zero intensity should
not be taken as evidence against the gap scenario. The finite intensity in the gap is also responsible for the
non zero density of states at E D . The integrated intensity for the data of Figs. 4.3(a,b) is shown in panel (e).
Though this one dimensional angle integrated intensity does not correspond to the density of states, which
is integrated over two dimensions, it gives some hint whether a gap is present. At high binding energy the
dispersion shows an almost linear behavior while near E D (indicated by broken line) it decreases. This shows
that near E D there are fewer states, a result that is in agreement with the gap scenario. When moving away
from the K point, the angle integrated intensity curve (black curve) show a larger anomalous region, which
is in agreement with a larger gap. The similarity between the cut through the K point and cuts away from
the K point where a gap definitely opens up further suggests that a gap is a more natural explanation for
the anomalous region, rather than the interaction between electrons and plasmons. It is very likely that the
non zero intensity is the result of the broad EDC peaks (Fig. 4.2(c)) which cause an overlap of the intensity
tails from the top of the valence band and the bottom of the conduction band. Another possible source of
such spectral weight may be due to edge states associated with the terrace or defect states 69 . Although at
this stage it is not clear why the EDC peaks are so broad, possible causes may be a self energy effect or
distribution of gaps. Finally regardless of the origin, what the large EDC width implies in terms of actual
device application remains to be seen in the future. One should note that ARPES lifetime determined as the
inverse line width tends to underestimate the transport lifetime by as much as two orders of magnitude 70 ,
and that in general one would expect a sharpening up of peaks as they are brought to the Fermi level, as
would happen in device applications.
Finally, the direct comparison between the two cuts in Fig. 4.3 allows to define a way to confidently
determine the presence of a gap in the spectra and to extract the size of such gap. This can be done from
26