Electronic localization in rotated graphene multi-layer

Rotated graphene bilayers show an interesting electronic structure with a tendency to layer decoupling at large rotation angles and a stronger electronic mixing at small angles, associated with a strong decrease of the velocity ([1] and Refs. therein). These inter-layer mixed states allow us [2] to address the long lasting problem of the origin of the Moir\'{e} pattern observed on STM images. For large and intermediate rotation angles, we present analytical and numerical studies of the local density of states in the Moir\'{e} that compare well to STM spectra. For very small angles, the inter-layer mixed states ultimately lead to electronic confinement in AA stacking regions in an energy range close to the Dirac point. In graphene multi-layer (up to 10 layers) containing twisted intercalated layers [3], we found both bands with a strong velocity reduction, and bands without velocity reduction. This could explain [2] why velocity renormalization is not observed experimentally in rotated multi-layers on SiC [3,4]. \\[4pt] [1] G. Trambly de Laissardi\`{e}re et al., Nano Lett. 10, 804 (2010). \\[0pt] [2] G. Trambly de Laissardi\`{e}re et al., in preparation. \\[0pt] [3] M. Sprinkle et al., J. Phys. D: Appl. Phys. 43, 374006 (2010). \\[0pt] [4] M. Sprinkle et al., Phys. Rev. Lett. 103, 226803 (2009).