Hofstatder Physics and Many-body Interactions in Twisted Bilayer Graphene

Twisted bilayer graphene (TwBLG) consists of two twistingly stacked sheets of graphene spaced only 0.34 nm apart. The interlayer interactions in TwBLG are strongly dependent on the twist angle and can vastly affect the electronic properties of the system. Recently, we have experimentally observed the existence of novel insulating states in TwBLG with small twist angles, which result from the interplay between interlayer hybridization and the periodicity of the underlying moir\'{e} pattern[1]. However, the transport gaps of the insulating states are much larger than existing theory predictions, suggesting possible effects of many-body interactions and/or mechanical effects. Additionally, we also observe for the first time the Hofstadter butterfly in TwBLG with a sub-degree twist angle in a high magnetic field, where the quantum Hall effect in this regime shows major differences compared with previously measured samples. [1] Y. Cao, J. Y. Luo, V. Fatemi, S. Fang, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Phys. Rev. Lett. 117, 116804 (2016).