Collaboration with P. Mallet & J.-Y. Veuillen (QNES group @ Institut Néel), D. Mayou (SIN group @ Institut Néel), G. Trambly de Laissardière (LPTM, Université de Cergy-Pontoise), V. Renard & C. Chapelier (CEA-INAC), I.Brihuega & J.M.Gomez-Rodrigues (UAM Madrid).
The unique electronic properties of graphene are a consequence of its honeycomb lattice : a triangular lattice with two equivalent atoms per unit cell. If two or more of these honeycomb lattice layers are stacked on top of each other, graphene electronic features —linear dispersion, chirality— can be lost. This has been known for years in graphite but also for bilayers (Fig. 1) with either AA (all atoms on top of each other) or AB (stacking similar to graphite) bilayers. Other types of stacking can be found for example for graphene multilayers grown on the C face of SiC but also on Ni or graphene flakes on graphite where the two layers are rotated with respect to each other. Rotation generates moiré pattern.
|Figure 1 : Moiré pattern generated by a rotation between two graphene layers. Dash (full line) cercle AA (AB) stacking region.|
The modulation of the local environment due to the rotation, generates an additional potential with a larger period that is superimposed to graphene and can change its electronic structure. In the case of graphene on metal systems, the superpotential can induces additional Dirac cones or gaps. In the case of rotated graphene bilayers, we have shown that the effect is strongly angle dependent. To address the very large supercell involved in this study, we developed a tight binding scheme based on the ab initio calculations.
At large rotation angle, the rotated bilayer behaves like two isolated graphene layers. For decreasing angles, states from Dirac cones belonging to each of the two carbon layers interact in an energy range that comes closer to the Dirac energy. In the vicinity of the crossing point a gap opens. At 2D, saddle points related to gaps create strong peaks in the density of states : the so-called van Hove singularities. Our theoretical predictions of van Hove singularities and of their energy position for varying rotation angles are in agreement with STM/STS experiments for graphene on Ni (E.Andrei’s group) and graphene on the C face of SiC.
|Figure 2 : Van Hove sigularities in a rotated graphene bilayer. a) principal, b) band structure and DOS. The DOS is calculated using our TB scheme, the band structure compares graphene mono (black) and rotated bi (red) layer dispersions and the DFT (dots) and the TB (line) results. It shows the band renormalization and the opening of gaps at the crossing points (M point).|
The electronic structure of a rotated graphene bilayer evolves from the electronic structure of two decoupled layers to renormalisation of the velocity at the Dirac point, localization when the two vHs merge ( 2°) and confinement in the AA stacked regions for smaller angles.
|Figure 3 : a) Ratio of the velocities at Dirac energy of the bilayer on the monolayer as a fonction of the rotation angle. b) DOS that shows confinement peaks at very small rotation angles in the AA region.|
We are now working on the effect of asymmetric doping and small angle (close to 2°) regime.
G. Trambly de Laissardière, D. Mayou, L. Magaud. Numerical studies of confined states in rotated bilayers of graphene. Phys. Rev. B 86, 125413 (2012)
I.Brihuega et al. Unravelling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene. Phys. Rev. Lett (2012)
G. Trambly de Laissardière, D. Mayou, L. Magaud. Localization of Dirac electrons in rotated graphene bilayers. Nano Lett. 10, 804 (2010)
J. Hass et al. Why multilayer graphene grown on the SiC(000-1) C-face behaves like a single sheet of graphene. Phy. Rev. Lett. 100, 125504 (2008)