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Supplementary Information
1. Sample preparation and characterization
The HOPG and NSCG samples, mounted on Si(111) substrates, were cleaved using
sticky tapes, transferred immediately into the measurement chamber, and annealed at 650 ˚C for
several hours by passing a current through the Si substrate. The Si-terminated SiC(0001) sample,
of the 6H polymorph, was cleaned in air by exposure to ozone generated by an ultraviolet lamp.
Once transferred into the measurement chamber, it was outgassed by passing a current through
the sample itself. Various surface reconstructions and graphene layer configurations were
prepared by high temperature treatment and characterized by reflection high energy electron
diffraction.
HOPG, upon cleavage, can yield an inhomogeneous surface with varying densities of
defects including steps. It is important to ascertain the sample quality within the spot of
illumination during the photoemission measurements. For each cleave in our experiment, survey
ARPES spectra were taken at different positions on the surface. The results were generally
consistent, but with different levels of background emission and sharpness of the primary
ARPES features. Occasionally, much worse spots could be found. The results are explained in
terms of scattering by defects of the primary electrons leading to a secondary electron
background and smearing of the primary ARPES features. As an example, Fig. S1 shows normal
emission spectra obtained at four different spots, P1-P4, on one HOPG sample, using 22 and 26
eV photons [S1]. Through experimentation with a larger number of samples and spots, we
conclude that spectra like those from P1 and P2 are about the best that can be obtained and must
be close to being intrinsic for HOPG. Emission from the gap region at normal emission (Fig.
S1(c)) indicates that there is a correlation between the intensity of the background emission and
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the height of the Fermi edge in each case. The step height associated with the gap remains the
same for the cases P1-P3. For P4, the gap is no longer apparent due to the high background
emission. Because of the small crystallite sizes in HOPG, some defect emission is inevitable.
This might explain the residual Fermi edge in the best spectra.
2. Symmetrization of photoemission spectra
Some of the photoemission spectra presented in our paper are symmetrized by adding
each spectrum to its mirror image about the Fermi level. This symmetrization procedure has been
employed by others in the analysis of the superconducting gap in high-temperature
superconductors. The results highlight gap features near the Fermi level, and mimic what one
might observe with scanning tunneling spectroscopy. In the present case, symmetrization
removes the Fermi edge derived from impurity and defect scattering. This procedure is especially
helpful when impurity and defect scattering is intense. As an illustration, Fig. S2 shows a Fermi
edge, its mirror image about the Fermi level, and the sum. The sum, i.e., the symmetrized
spectrum, is just a straight horizontal line.
3. Evidence of secondary gaps induced by in-plane phonons
The dipole transition term is suppressed, but nonzero. It allows coupling with in-plane
phonons at the K point in the Brillouin zone, thus contributing to the normal emission spectrum.
The four in-plane phonon modes clustered around 150 meV should give rise to a gap feature,
however weak. Indeed, data taken from HOPG (Fig. S3(a,b)) show evidence of a very weak
onset at ~150 meV, signifying a gap. The straight line (Fig. S3(a)) is a linear fit to the data below
-0.25 eV, and the green curve is the result of fitting assuming two gaps. The resulting gap
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positions, 64 and 153 meV, are indicated by vertical dashed lines. As further evidence, the
absolute value of the first derivative of the spectrum (Fig. S3(c)) shows two peaks at the gap
positions. The gap at 153 meV should actually consist of three closely spaced gaps
corresponding to the K2, K5 (doubly degenerate), and K1 modes at approximately 124, 151, and
164 meV, respectively, based on our calculations (see Fig. 1 (c,d)), but we have not been to
resolve them.
4. Gaps in epitaxial graphene layers thicker than 5 ML
Epitaxial graphene layers on SiC(0001) can be produced by heating the sample to
evaporate away the Si atoms near the surface [S2]. Thicker graphene layer stacks are obtained by
heating the sample to higher temperatures (up to ~1450°C) and/or for longer periods. The surface
roughens appreciably at graphene coverages higher than about 3 ML [S3]. Normal emission
spectra (Fig. S4(a)) for the 6 3  6 3 surface and graphene layers of various thicknesses show
that the peak at about -4.3 eV derived from the σ band becomes less pronounced beyond 3 ML
(Fig. S4(a)), suggesting increased surface roughness. However, emission from the π band near
the K point (Dirac cone region) for the surface covered with >5 ML graphene (inset in Fig.
S4(a)) remains graphite-like. The increased roughness results in a less obvious gap (Fig. S4(b)).
The absolute first derivative of the spectrum (Fig. S4(b)) shows peaks at the edges of the gap as
expected. The filling in of the gap can be attributed to defect scattering that smears out the
phonon spectrum. An equivalent view is that momentum conservation is no longer strictly
obeyed, and phonons away from the K point in the Brillouin zone can also contribute to phononassisted photoemission at normal emission.
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References:
[S1] A. R. Law, M. T. Johnson, and H. P. Hughes, Phys. Rev. B 34, 4289 (1986).
[S2] K. V. Emtsev, F. Speck, Th. Seyller, L. Ley, and J. D. Riley, Phys. Rev. B 77, 155303
(2008).
[S3] T. Ohta, A. Bostwick, Th. Seyller, K. Horn, and E. Rotenberg, Science 313, 951 (2006).
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(c)
Intensity (arb. units)
h = 22 eV
h = 22 eV
P1
P2
P3
P4
Intensity (arb. units)
(a)
Intensity (arb. units)
(b)
h = 26 eV
P1
P2
P3
P4
P3
P2
P1
-12 -10
-8 -6 -4
Energy (eV)
-2
0
-0.4
-0.2
0.0
Energy (eV)
0.2
FIG. S1. Position dependent normal emission spectra from HOPG. (a) Normal emission spectra
of HOPG taken at 22 eV from four different spots, P1-P4, on the same sample. (b) Similar data
taken at 26 eV. The red vertical dash line marks the band edge of graphite. (c) Detailed view near
the Fermi level of the spectra taken at 22 eV. Spectra in (c) have been shifted vertically for
clarity. The zero level for each spectrum is indicated by a tick mark on the right vertical axis.
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Intensity
1.0
0.5
F(E)
F(-E)
F(E)+F(-E)
0.0
-200
-100
0
100
Energy (meV)
200
FIG. S2. Symmetrization of the Fermi-Dirac function F  E  for an assumed temperature of 60
K. The result is a horizontal line. Zero energy corresponds to the Fermi level.
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(a)
Intensity (arb. units)
HOPG
(h = 22 eV)
Expt
Linear Fit (<-0.25 eV)
Fit with two phonon modes
-0.8
-0.6
-0.4
Energy (eV)
Intensity (arb. units)
First derivative (arb. units)
(b)
-0.3
-0.2
-0.1
0.0
Energy (eV)
0.1
-0.2
0.0
(c)
-0.3
-0.2
-0.1
0.0
Energy (eV)
0.1
FIG. S3. Normal-emission spectrum from HOPG showing gaps induced by out-of-plane and inplane phonons. (a) Integrated normal-emission spectra taken from multiple scans. The red line is
a linear fit to the data at energies below –0.25 eV, and the green curve is a model fit assuming
two gaps. The vertical dash lines indicate positions of the Fermi level and the two gaps. (b) A
zoom-in view of the spectrum near the gap edges. (c) Absolute value of the first derivative of (b).
The zero level for each spectrum is indicated by a tick mark on the right vertical axis.
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h = 50 eV
(b)
0
>5 ML
(FD)

-0.2
0.2
0.0
-1
k - K (Å )
>5 ML
4 ML

3 ML
Intensity (arb. units)
Intensity (arb. units)
-1
>5 ML (S)
>5 ML
2 ML
First Derivative (arb. units)
Energy (eV)
(a)
1 ML
6 3
-12
-10
-4
-6
-8
Energy (eV)
-2
0
-0.3 -0.2 -0.1 0.0 0.1 0.2
Energy (eV)
FIG. S4. Gap in epitaxial graphene layers beyond 5 ML. (a) Evolution of normal emission
spectra as a function of graphene layer coverage. The inset shows the π band near the K point
for the surface with >5 ML graphene. The measurement direction is perpendicular to ΓK . (b) A
normal emission spectrum, its symmetrized version, and the absolute value of its first derivative
(FD) for the surface with >5 ML graphene. The zero level for each spectrum is indicated by a
tick mark on the right vertical axis.