Resonance Raman Spectroscopy of G-line and Folded Phonons
in Twisted Bilayer Graphene with Large Rotation Angles
Supplementary Online Material
Methods
Bilayer graphene synthesis. Graphene was grown by CVD of CH4 on Cu foils (25 μm in
thickness) at ambient pressure. Cu foils were annealed at 1050 °C for 30 min in H 2 atmosphere
before graphene growth. The CVD parameters were optimized to grow mostly bilayer graphene
gains1. Specifically, bilayer grains were grown at 950 °C under 20-30 ppm CH4 balanced in H2
and Ar with a total flow rate of 1500 sccm (1.3% H2). Growth time was carefully controlled to be
20-30 min in order to avoid growth of any continuous film. After growth, graphene samples were
transferred by the PMMA-assisted wet-transfer method. The procedure is similar to those
previously reported in Ref. 2 and 3. An aqueous solution of iron nitrate (0.1 g/ml) was used as a
Cu etchant. Bilayer and few-layer graphene can be preferentially grown on Cu substrates in the
circumstance of excess of supplied active carbon, e.g., with a relatively high concentration of
CH4 introduced during the CVD of graphene process.
1
S. Nie, W. Wu, S. R. Xing, Q. K. Yu, J. M. Bao, S. S. Pei, and K. F. McCarty, New J. Phys. 14,
093028 (2012).
2
W. Wu, Z. H. Liu, L. A. Jauregui, Q. K. Yu, R. Pillai, H. L. Cao, J. M. Bao, Y. P. Chen and S.
S. Pei, Sensors and Actuators B 150, 296–300 (2010).
3
W. Wu, Q. K. Yu, P. Peng, Z. Liu, J. M. Bao and S. S. Pei, Nanotechnology 23, 035603
(2012).
TEM investigation. TEM samples were prepared using the TEM grids with amorphous Si3N4
window. TEM studies including conventional TEM, high resolution TEM and microdiffractions
were conducted using a FEI Tecnai F20 analytical microscope operated under the acceleration
voltage of 200 kV with a point-to-point resolution of 0.16 nm.
Raman characterization. Raman measurements were performed with three different systems at
room temperature. Two of them are commercial micro-Raman spectrometers: XploRA (Horiba)
and T64000 (Horiba). The XploRA is equipped with two laser lines at 638 nm (1.94 eV) and 532
nm (2.33 eV). The T64000 is equipped with three lines at 514 nm (2.41eV), 488 nm (2.54eV)
and 458 nm (2.71eV). Both systems are equipped with 100× objectives and automatic XYZ
stages capable of Raman mapping. The UV micro-Raman scatterings were performed with a
home-built system that consists of an iHR 320 spectrometer (Horiba) and an Argon ion laser at
363 nm (3.41 eV). To reduce laser heating, the laser power was reduced below 2 mW during all
the measurements.
Phonon calculations. The phonon calculations were performed using the generalized-gradient
approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional, and
the norm-conserved pseudopotential plane-waves as implemented in the Quantum Espresso
suite4. The code allows phonon frequencies and eigenvectors to be calculated at arbitrary qvector in the Brillouin zone (BZ) within the linear response density functional perturbation
theory (DFPT)5. The electronic band structure, related properties, and geometry optimization of
the structures were calculated self-consistently (SCF) with 100 Ry kinetic energy cutoff for the
plane wave, 400 Ry charge density cut-off, SFC tolerance better than 10−8, and phonon SFC
threshold of 10-14. The phonons were calculated for various q-vectors in the BZ of a single layer
(1L) graphene. The q-vectors corresponding to the Moiré lattice of tBLG with twisting angle θ
and length 𝑞(𝜃) =
4
𝜃
8𝜋
√3𝑎
𝜃
sin ( 2) was mapped onto the 1L BZ at fractional coordinates given by
4
𝜃
[ sin ( 2) sin(60 − 𝜃), sin ( 2) sin(𝜃), 0]. The phonon dispersion is presented as calculated
√3
√3
without the corrections for electron-electron interactions that are typically accounted for by using
Green function GW methods6. These corrections are important for q-vectors larger than those at
the cross points of the LO and TO dispersion of the G-mode. The q-vectors that are reachable in
the Raman experiment lay within the dispersion space that is well described by DFPT.
4
P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L.
Chiarotti, M. Cococcioni, I. Dabo, et al., J. Phys.: Cond. Mat. 21, 395502 (2009).
5
S. Baroni, S. de Gironcoli, A. dal Corso and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001).
6
M. Lazzeri, C. Attaccalite, L. Wirtz and F. Mauri. Phys. Rev. B 78, 081406 (2008).
(a)
27.8o
(b)
2 nm
SOM 1. Transmission electron microscopy (TEM) diffraction (a) and high-resolution lattice
image (b) of twisted graphene with a rotation angle of ~ 27.8 degrees, which is the largest
rotation angle for commensurate lattices with a minimum supercell.
(a)
~12o
(b)
~4o
2 nm
2 nm
10
(c)
VHS
8
dI/dV (S)
dI/dV (S)
8
10
6
4
2
0
~12o
-1.5 -1.0 -0.5 0.0 0.5 1.0
Sample bias (V)
VHS
6
4
2
1.5
(d)
0
~4o
-1.5 -1.0 -0.5 0.0 0.5 1.0
Sample Bias (V)
1.5
SOM 2. Lattice images and dI/dV curves of tBLG using scanning tunneling microscopy (STM).
(a-b) Moiré patterns revealed by STM imaging. The rotation angles between graphene layers are
calculated from Fast Fourier Transform (FFT) analysis of the Moiré patterns. (c-d):
Corresponding dI/dV curves. The twist dependent Van Hove singularity (VHS) can be observed
in both tBLG domains.