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

Chapter 4
Gap opening in epitaxial graphene
Graphene is considered one of the most exciting materials in solid-state physics. Since its discovery
in 2004 a variety of novel phenomena have been discovered and predicted, from an anomalous quantum
Hall effect 51,52,53 , ballistic transport 5 , easy control of charge carriers by externally applying voltage 5 , half
metallicity 54 , Kondo physics 55,56,57 , superconductivity 58,59,60 etc. The secret to all of these fascinating
phenomena lies in the unique nature of the electronic properties of graphene, where the low energy excitations
resemble massless Dirac fermions. Although several experiments have shown results in agreement with the
existence of Dirac fermions, so far direct experimental evidence has been limited. Here we present a detailed
study of the electronic structure of graphene by using ARPES. How this evolves from single layer graphene to
infinite layers graphite is also discussed. In general graphene can be obtained by rubbing a piece of graphite
on a SiO 2 surface 5,61 . This method however gives rise to very small samples of the order of few microns,
which are difficult to investigate with ARPES, where the average beam size is of the order of 100 micron.
The graphene samples we have investigated are epitaxial graphene grown by thermal decomposition of a SiC
single crystal 62 . As we will discuss below, the resulting graphene layer is tightly bounded with the substrate.
The graphene-substrate interaction will modify the Dirac cone by inducing a gap between the conduction
band and the valence band, making it an ideal candidate for next generation electronic devices.
4.1 Dirac fermions in epitaxial graphene
Figs. 4.1(a-c) show ARPES intensity maps at constant energies of E F , -0.4 eV and -1.2 eV. At E F (panel
a), the intensity map shows a finite and almost circular contour centered around the K point. As the binding
energy increases, the contour first decreases in size and becomes a point at -0.4 eV (panel b). Beyond -0.4
eV, the size of the contour expands again. This behavior is consistent with the presence of Dirac fermions,
where a conical dispersion centered at the K point is expected. The Dirac point energy is shifted to 0.4 eV
below E F , which shows that the as-grown graphene is electron-doped 48,63 . At higher binding energy (panel
c) the high intensity region in the intensity map deviates from the circular shape. Similar trigonal distortions
have been reported for graphite 64 . Note that the intensity along the circular contour is not isotropic and is
strongly suppressed on the left (first BZ) for energy above the Dirac point energy (panel a) and on the right
(second BZ) for energy below the Dirac point energy (panel c). This is a well-known effect in graphite and
is due to the ARPES dipole matrix element which suppresses or enhances the intensity in different BZs 65 .
Fig. 4.1(e) shows the overall dispersion of the π bands measured for a symmetric cut through the K point.
Following the maximum in the intensity plot, two cones dispersing in opposite directions (one upward and
another downward) can be clearly distinguished, in overall agreement with the presence of Dirac fermions.
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