Symmetry Breaking in Few Layer Graphene Films Page: 2 of 23
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Symmetry Breaking in FLG Films
Figure 1. Atomic arrangement in (left) monolayer and (right) bilayer graphene. The
inset shows the unit cell with two equivalent atoms.
on various substrates. Forbeaux et al. were the first to demonstrate that high-quality
epitaxy of single and few-layer graphene (FLG) could be achieved on the silicon-rich
SiC(0001) surface. Transport measurements and demonstration of the feasibility of
patterned graphene devices were demonstrated by Berger et al. [7, 8].
Fig. 1 shows the atomic arrangement in monolayer and bilayer of graphene. The
unit cell consists of two equivalent C atoms, labelled A and B with bond length
1.42 A. Jones proved that for a closed-packed hexagonal lattice, the energy gap along
the zone boundary disappears where bands from adjacent unit cells cross . This
is illustrated in Fig. 2, which shows the tight-binding (TB) band structure E(k) of
graphene, evaluated to third nearest neighbor using the parameters of Reich . (Here
we restrict consideration to the r and the r* states, which are derived from the pz
orbitals of the carbon atoms). Quantitative fits of the TB model to experimentally
determined bands were presented by Bostwick et al. (Ref. ). These states meet at
the so-called Dirac crossing point at energy ED in agreement with Jones' theorem. For
neutral (undoped) graphene, the Fermi energy (the energy of the least-bounds states)
Many of the interesting properties of graphene revolve around the fact that the band
crossing at ED is strictly gapless. This means that at zero doping and zero temperature,
graphene is a gapless semiconductor or a zero-overlap semimetal. Upon doping the
graphene by either deposition of foreign atoms [13, 14], molecules  or in a gated
geometry [1, 2, 3], the carrier density can be easily manipulated. With this control,
we can systematically study the many-body interactions in graphene as a function of
doping using angle-resolved photoemission spectroscopy.
1.2. Angle-resolved Photoemission Spectroscopy
The Fermi surface is defined as a constant energy surface E(k)EEF, and determines
all the transport properties of conducting materials. While transport measurements on
doped graphene can determine the relevant properties such as group velocity and lifetime
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Bostwick, A.; Ohta, T.; McChesney, J.L.; Emtsev, K.; Seyller,Th.; Horn, K. et al. Symmetry Breaking in Few Layer Graphene Films, article, May 25, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc900224/m1/2/: accessed July 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.