Electronic localization in small-angle twisted bilayer graphene

Close to a magical angle, twisted bilayer graphene (TBLG) systems exhibit isolated flat electronic bands and, accordingly, strong electron localization. TBLGs have hence been ideal platforms to explore superconductivity, correlated insulating states, magnetism, and quantized anomalous Hall states in reduced dimension. Below a threshold twist angle ($\sim$ $1.1^\circ$), the TBLG superlattice undergoes lattice reconstruction, leading to a periodic moir\'e structure which presents a marked atomic corrugation. Using a tight-binding framework, this research demonstrates that superlattice reconstruction affects significantly the electronic structure of small-angle TBLGs. The first magic angle at $\sim$ $1.1^\circ$ is found to be a critical case presenting globally maximized electron localization, thus separating reconstructed TBLGs into two classes with clearly distinct electronic properties. While low-energy Dirac fermions are still preserved at large twist angles $> 1.1 ^\circ$, small-angle ($\lesssim 1.1^\circ$) TBLG systems present common features such as large spatial variation and strong electron localization observed in unfavorable AA stacking regions. However, for small twist angles below $1.1 ^\circ$, the relative contribution of the local AA regions is progressively reduced, thus precluding the emergence of further magic angles, in very good agreement with existing experimental evidence.