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An unconventional insulating phase and a superconducting phase were recently discovered in the twisted bilayer graphene [Y. Cao et al, Nature 556, 80; 556, 43 (2018)], but the relevant low-energy electronic states have not been clearly identified yet. In this work, I show that the interlayer hopping induces a spatially modulated Dirac mass term in the continuum Hamiltonian, and leads to a low-energy band formed by Dirac zero modes in the moire superlattice. This moire band becomes extremely flat and thus strongly correlated when the Dirac velocity vanishes approaching the magic angle, and enters a quantum disordered Mott insulating phase at 1/4 and 3/4 filling, i.e., +-2 excess electrons per moire supercell, which may account for the insulating phase discovered in experiments. This model should be a good starting point for studying the exotic superconducting phase in slightly doped twisted bilayer graphene.
Long Zhang received his bachelor's degree in 2010 and doctorate in 2015 from Tsinghua University. After two years' postdoctoral research in Peking University, he joined Kavli Institute for Theoretical Sciences in University of Chinese Academy of Sciences as a junior faculty. His research focuses on the theoretical understanding of correlated electron materials, topological states of matter and unconventional phase transitions.