Supplementary Online Material s1

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 H2 atmosphere before graphene growth. The CVD parameters were optimized to grow mostly bilayer graphene 1 gains . 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.

1S. 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). 2W. 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). 3W. 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 q- vector 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 was mapped onto the 1L BZ at fractional coordinates given by . The phonon dispersion is presented as calculated 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. 4P. 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). 5S. Baroni, S. de Gironcoli, A. dal Corso and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001). 6M. Lazzeri, C. Attaccalite, L. Wirtz and F. Mauri. Phys. Rev. B 78, 081406 (2008). (a) 27.8o (b)

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 10 VHS 8 (c) VHS 8 (d) ) ) S S ( ( 6 6

d / / I I

d 4 4 d

2 o 2 ~12 ~4o 0 0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Sample bias (V) Sample Bias (V)

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.