Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers

The methods for realizing of non-Abelian gauge potentials have been proposed in many different systems in condensed matter1-5. The simplest realization among them may be in a graphene bilayer obtained by slightly relative rotation between the two layers4. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunnelling microscopy and spectroscopy. At a magic twisted angle, theta ~ (1.11+/-0.05)deg, a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, are observed in the tunnelling density of states due to the action of the non-Abelian gauge fields4,6-8. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunnelling peaks with energy spacing detal E ~ vF/D ~ 70 meV (here vF is the Fermi velocity of graphene and D is the period of the Moire patterns). Our results direct demonstrate that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the Moire patterns.