Supplementary information for
Electronic Structures of Graphene Layers on a Metal Foil: The
Effect of Atomic-scale Defects
Hui Yan1,§, Cheng-Cheng Liu2,3,§, Ke-Ke Bai1,§, Xuejiao Wang2, Mengxi Liu4, Wei Yan1, Lan
Meng1, Yanfeng Zhang4,5, Zhongfan Liu4, Rui-fen Dou1, Jia-Cai Nie1, Yugui Yao2,a, and
Lin He1,b,*
3
1
Department of Physics, Beijing Normal University, Beijing, 100875, People’s Republic of China
2
School of Physcis, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of
Sciences, Beijing 100190, People’s Republic of China
4
Center for Nanochemistry (CNC), College of Chemistry and Molecular Engineering, Peking University, Beijing
100871, People’s Republic of China
5
Department of Materials Science and Engineering, College of Engineering, Peking University, Beijing 100871,
People’s Republic of China
§
These authors contributed equally to this paper.
*Email: helin@bnu.edu.cn.
I. Experimental method: The structure and electronic properties of the point defects were
studied by scanning tunneling microscopy and spectroscopy (STM and STS). The STM system
was an ultrahigh vacuum four-probe scanning probe microscope from UNISOKU. All STM and
STS measurements were performed at liquid-nitrogen temperature and the images were taken in
a constant-current scanning mode. The STM tips were obtained by chemical etching from a wire
of Pt(80%) Ir(20%) alloys. Lateral dimensions observed in the STM images were calibrated
using a standard graphene lattice. The STS spectrum, i.e., the dI/dV-V curve, was carried out
with a standard lock-in technique using a 957 Hz alternating current modulation of the bias
voltage.
II. Other experimental results
Figure S1(a) shows a STM image of a flat area of the as-grown graphene monolayer on
polycrystalline Rh foil, which does not show periodic moiré superstructures. This feature differs
quite from that of the graphene monolayer on a (111) surface of single-crystal Rh [S1-S4]. For the
graphene monolayer on a (111) surface of single-crystal Rh, the strong C-Rh covalent bond and
the lattice mismatch between graphene (0.246 nm) and Rh(111) (0.269 nm) could lead to
hexagonal moiré superstructures with the periodicity of 2.9 nm.S1-S4 The absence of moiré
superstructures, as shown in Fig. S1(a), indicates that the coupling between graphene and the Rh
foil is much weaker than that of monolayer graphene on a single-crystal Rh. Fig. S1(b) and Fig.
S1(c) show atomic resolution STM images of the graphene, where a clear honeycomb lattice is
observed. Fig. S1(d) shows a typical STS spectrum of the sample. The tunnelling spectrum gives
direct access to the local density of states (LDOS) of the surface at the position of the STM tip.
The linear DOS around the Dirac point ED consists well with that of the pristine graphene. The
position of the Dirac point ED is slightly above the Fermi level, suggesting charge transfer between
the graphene and the substrate. Similar result about the as-grown graphene monolayer on the Rh
foil was reported in a previous paper.S5
Figure S1. (a) A STM topographic image of the as-grown graphene monolayer on
polycrystalline Rh foil. (Vsample = 377 mV and I = 65.0 pA). (b) Atomic-resolution image of
graphene in the white frame of panel (a) (Vsample = 204 mV and I = 13.1 pA). (c) Enlarged
atomic-resolution image of the graphene monolayer. The atomic structure of graphene is overlaid
onto the STM image. (d) A typical tunneling spectrum, i.e., dI/dV-V curve, recorded on the
graphene monolayer. The Dirac point as marked by the black arrow, is located at ED ~ 38 mV,
indicating a slight charge transfer between the graphene and substrate. A round the Dirac point,
the density of states increases linearly with the energy, which is identical to that in pristine
graphene. The dashed line is a guide to the eyes.
Figure S2. (a) A STM image of a flower defect in graphene monolayer on polycrystalline Rh foil
(Vsample = 271 mV and I = 1.98 pA). (b) Atomic-resolution image in the white frame of panel (a)
(Vsample = 271 mV and I = 1.98 pA). The structure of graphene is overlaid onto the STM image. (c)
The FFT image of panel (a). (d) The enlarged FFT image in panel (c). The outer six spots
represent the intervalley scattering wave vectors q2. The inner six spots correspond to the
reciprocal lattice vector of the flower defect. The inner bright spot centered at the  point arise
from the intravalley scattering.
Figure S3. (a) A STM topographic image of a point defect in graphene monolayer on
polycrystalline Rh foil. (Vsample = 248 mV and I = 34.5 pA). (b) A typical tunneling spectrum, i.e.,
dI/dV-V curve, recorded on the defect. A localized defect state is observed at ~ 130 mV. The
energy of the localized states depends on the type of defect in graphene.
Figure S4. (a) A three-dimensional topography of a deformed structure in a twisted graphene
bilayer on Rh foil (Vsample = 640 mV and I = 7.71 pA). (b) The FFT image of panel (a). The outer
six spots represent the intervalley scattering wave vectors q2. The inner six spots correspond to the
reciprocal lattice vector of the Moire pattern.
III. Analysis of the effects of point defects on electronic properties of grapheme
To further explore the effects of point defects on electronic properties of graphene,
first-principles calculations using the projector augmented wave pseudopotential method and
Perdew-Burke-Ernzerhof exchange-correlation potentialS6 implemented in the VASP packageS7
have been carried out. The STM simulations are performed using the Tersoff-Hamann model.S8
The supercell of graphene can be divided into two categories, i.e., a 3n×3n (n = 1,2,3…)
supercell with valleys K and K′ folded into the point and a non-3n×3n supercell with valleys
separated in the momentum space. In the calculation, we select the flower defect, which has a
well-defined atomic structure, as a typical structure of the point defects. Two typical
configurations, which include one defect in a 8×8 supercell (Fig. S5(a)) and one defect in a 9×9
supercell (Fig. S5(e)), are considered. Fig. S5(b) and Fig. S5(f) are the simulated STM images
around the flower defect of the 8×8 and 9×9 supercell respectively. Both of them show a
3  3R30 interference pattern of carbocyclic rings around the defect, which consists well with
our experimental results (see Figure S6 for more simulated STM images). However, the electronic
band structures of the two configurations are quite different, as shown in Fig. S5(c) and S5(g). The
8×8 supercell remains linear band dispersion around the K point, while the 9×9 counterpart opens
a gap with the minimum at the point.
The emergence of a significant gap in defect superlattice arises from the fact that the 9×9
supercell hybridizes the two independent Dirac points: both K and K′ of the pristine graphene are
folded back to the center of the supercell, as shown in Fig. S5(h). The randomly distributed
point defects will weaken the mixture of the two valleys and reduce the gap.S9 As a consequence,
the electronic band structure of our sample, which shows complete random distribution of the
point defects, should resemble that obtained from a non-3n×3n supercell calculation. For the case
of the 8×8 supercell, the K (K′) of the pristine graphene is folded to K′(K) of the 8×8 supercell
(Fig. S5(d)). Therefore, the 8×8 supercell has a similar linear band structure as the pristine
graphene but with a much reduced Fermi velocity ~ 4.78×105 m/s, as shown in Fig. S5(c).
Whether the defect superlattice with a 3n×3n supercell will or not open a gap in graphene can
be understood more generally from the symmetry point of viewS10 and the obtained result should
be independent of the type of point defects. It suggests that we can tune the electronic structures of
graphene by controlling the density of the point defects and it’s possible to realize all-graphene
electronics once that the point defects can be patterned into graphene in a controllable way.
Figure S5. (color online). (a) and (e) show two typical configurations, which are one flower defect
in a 8×8 and one flower defect in a 9×9 supercell, respectively. The atomic structure of the flower
defect is shown in yellow. (b) and (f) show the simulated STM images at ~ 500 meV sample bias
around the flower defect of panel (a) and (e) respectively. (c) and (g) show electronic band
structures of the two configurations in panel (a) and (e) respectively. (d), (h) Brillouin zone for
graphene (red borders) and Brillouin zones for the 8×8 supercell and 9×9 supercell (black
borders). The center  and two inequivalent corners K and K′ of the Brillouin zones are also
indicated for the analysis in the text.
Figure S6. The simulated STM images around the flower defect at different bias. The simulation
integrates the energy from (a) EF - 0.5 eV to EF, (b) EF to EF + 0.1 eV, (c) EF + 0.3 eV to EF + 0.5
eV , and (d) EF + 0.4 eV to EF + 0.6 eV (EF is the Fermi level).
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