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

Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ≈(1.11±0.05)^∘, a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δE≈vF/D≈700.16em0exmeV (here vF is the Fermi velocity of graphene and D is the period of the moir\'e patterns). This indicates 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 moir\'e patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 10⁶0.16em0exm/s to zero by simply reducing the twisted angle of about 2^∘.