Supplementary Information
Modulation of Fermi velocities of Dirac electrons in single
layer graphene by moiré superlattice
Q. Zou, 1, a) B. D. Belle, 2,b) L. Z. Zhang, 1, a) W.D. Xiao1, K. Yang1, L.W. Liu1,
G.Q.Wang1, X.M. Fei1, Y. Huang1, R.S. Ma1, Y. Lu3, P. H, Tan3, H.M. Guo1, b), S. X.
Du1, and H.-J. Gao1, b)
1
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2
School of Physics & Astronomy, University of Manchester, Oxford Road,
Manchester M13 9PL, UK
3
Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
Contents
1. Fabrication and characterization of graphene devices
2. Defects and impurities on graphene surface
3. Electron transport process in the STS measurement of graphene device
§
These authors contribute equally to this work.
*To whom correspondence should be addressed. Email: hmguo@iphy.ac.cn and
hjgao@iphy.ac.cn.
1. Fabrication and characterization of graphene devices
Monolayer graphene with dimensions of several tens of micrometers was prepared
by micromechanical exfoliation from natural graphite. It was subsequently transferred
onto an h-BN flake on 90 nm oxidized Si substrate using a dry transfer process, so
that the interface between the graphene and h-BN remains dry and free of polymer
contaminants1. Fig. S1a and S1b show the optical images of the graphene flake
transferred on the PMMA and h-BN substrates, respectively. In order to perform STM
measurement, an Au film (60 – 100 nm) and a Ti adhesion layer (4 nm) were then
deposited using a shadow mask technique as conductive contacts to the graphene
flake (Fig. S1c).
Before mounted into UHV chamber, the graphene device was inspected with
micro-Raman spectroscopy2, 3 using a Jobin Yvon HR800 system, with an excitation
laser energy of 2.36 eV (532 nm) and a laser power below 1 mW to avoid possible
sample damage induced by laser heating4. Fig. S1d shows a typical Raman spectrum
of graphene on h-BN. The most prominent features are four peaks, which refer to E2g
phonon mode of h-BN5 at 1367.3 cm-1, G and 2D bands of graphene at 1585.0 cm-1
and 2682.4 cm-1, and also a weak D peak at 1324.6 cm-1. Its 2D peak displays a single
Lorentzian line shape, and the intensity of 2D band is about three times of that of G
band. The Raman data shows a perfect feature of monolayer graphene6.
Figure S1 Fabrication and characterization of graphene devices. (a) Optical image of
exfoliating monolayer graphene flakes on 300 nm thick PMMA. (b) Graphene was subsequently
transferred from PMMA to an h-BN flake using a dry transfer process. (c) An Au film (60 - 100
nm) and a Ti adhesion layer (4 nm) were deposited as conductive contacts. In (a) to (c), the scale
bar is 25 μm, and the dash lines show the boundary of graphene flake. (d) Raman spectroscopy of
graphene/h-BN excited with laser energy of 2.36 eV. Three peaks refer to the Eg mode of h-BN at
1367.3 cm-1, G and 2D bands of graphene at 1585.0 cm-1 and 2682.4 cm-1.
2. Defects and impurities on graphene surface
We have performed STM imaging on more than ten areas of the graphene surface
on h-BN. Fig. S2a shows a typical topography image of the surface. Some impurity
adsorption can occur on the graphene surface or even under graphene layer. The
straight line indicates a linear defect. Most of point defects are about several
nanometers while some can be much larger. Fig. S2b and c give atomic resolution
STM images of small point defects in the graphene layer. Those defects can scatter
the tunneling electrons in graphene and reduce the mobility of sample.
In STS measurements, all the dI/dV spectra in our paper are obtained from the flat
areas of graphene, which are very far from the defects (distances greater than of 50
nm). The results demonstrate a high degree of spatial uniformity at flat areas on the
graphene/h-BN system.
Figure S2 STM topography images of single layer graphene on h-BN substrate. (a) Bright
points show impurities trapped under graphene layer or on the surface. The straight line indicates a
linear defect. Vb = -0.20 V, It = 16 pA. (b) Three bright areas indicate defects trapped under
graphene layer. Vb = -0.50 V, It = 10 pA. (c) Atomic resolution image shows some sharp point
defects and their electron scattering effect in graphene. Vb = -2. 0 V, It = 9 pA.
3. Electron transport process in the STS measurement of graphene device
If a bias voltage (e.g. a positive voltage) is applied on the sample under
perpendicular magnetic fields, there are two processes for electron transport from the
STM tip to Au metal electrode: 1) electrons tunnel locally from tip’s Fermi level into
Landau levels (LLs) of graphene, 2) tunneling electrons transport through single layer
graphene to Au electrode7.
During the second process, there are actually two type of states available to the 2D
electrons transporting through the inhomogeneous graphene layer, i.e. localized states
and extend states. The localized states are the bound states formed around the defects,
while the extended states are the states carrying the electric current across the sample.
Under lower magnetic field the separation of LLs is small. The scattering of tunneling
electrons around the defects in the “dirty” area of graphene into localized states makes
the STS curves featureless. Therefore, the absence of LLs under low magnetic field
may be due to the impurities adsorption and inhomogeneous carrier density in the
graphene sheet and the spectra is not perfect in this case.
Figure S3 Schematic of electron transport process in the graphene device under a magnetic
field. The electrons firstly tunnel locally into the LLs of graphene. During the transport process of
a tunneling electron through the graphene layer, it will encounter scattering by the defects in
graphene before its transport into Au electrode finally. The white point represents a defect on the
surface, such as impurities absorption, atomic defects, and so on.
When the magnetic field is increased, both the LLs spacing and the capacity of each
LL become larger, so that more electrons can tunnel into the LLs of graphene.
Additionally, as the magnetic length becomes small, electrons at extended states can
pass through the defects, carrying the current into Au electrode8, 9. The intrinsic LLs
of graphene are therefore easily resolved in STS measurement.
References
(1) Mayorov, A. S.; Gorbachev, R. V.; Morozov, S. V.; Britnell, L.; Jalil, R.; Ponomarenko, L. A.; Blake,
P.; Novoselov, K. S.; Watanabe, K.; Taniguchi, T.; Geim, A. K. Nano. Lett. 2011, 11, 2396-2399.
(2) Malard, L. M.; Pimenta, M. A.; Dresselhaus, G.; Dresselhaus, M. S. Phys Rep 2009, 473, 51-87.
(3) Ferrari, A. C. Solid State Commun. 2007, 143, 47-57.
(4) Tan, P. H.; Deng, Y. M.; Zhao, Q.; Cheng, W. C. Appl. Phys. Lett. 1999, 74, 1818-1820.
(5) Gorbachev, R. V.; Riaz, I.; Nair, R. R.; Jalil, R.; Britnell, L.; Belle, B. D.; Hill, E. W.; Novoselov, K.
S.; Watanabe, K.; Taniguchi, T.; Geim, A. K.; Blake, P. Small 2011, 7, 465-468.
(6) Ferrari, A. C.; Meyer, J. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang,
D.; Novoselov, K. S.; Roth, S.; Geim, A. K. Phys. Rev. Lett. 2006, 97, 187401.
(7) Chen, C. J., Introduction to scanning tunneling microscopy. Oxford University Press: New York,
1993; Vol. 227.
(8) Richard E. Prange, S. M. G., The quantum Hall effect. Springer-Verlag: New York, 1987.
(9) Jain, J. K., Composite fermions. Cambridge University Press: 2007.