Twisted bilayer graphene (TBG) consists of two stacked layers of graphene rotated relative to one another. With a twist angle of about 1.10° the so-called “magic” angle, many unconventional electronic behaviors emerge, including superconductivity and correlated insulators, a type of insulating phase that arises from interactions between electrons. Elucidating the mechanism responsible for these electronic states in magic-angle TBG is a problem at the frontier of quantum materials research. To help solve this problem, we employ an unbiased quantum many-body numerical method (quantum Monte Carlo simulations) to investigate the possible insulating phases of TBG.
Our large-scale simulations reveal a rich phase diagram, establishing the existence of three distinct insulating phases whose appearance can be controlled by tuning different types of interactions between the electrons. The first phase, called a quantum valley Hall state, has an insulating bulk and a dissipationless electronic current on its edge. The second phase, called an intervalley coherent state, is an insulator in which electron pairs emerge that behave in the same way as in a ferromagnet. The third phase, called a valence bond solid, is a phase realized in single-layer graphene if there were strong Coulomb interactions and electrons with degrees of freedom beyond just charge and spin (known as multiflavor electrons).
These results offer an unbiased solution for pristine TBG at charge neutrality, that is, the system has no extra electronic charge, and serves as the foundation for explanation of the more exotic behaviors of this fascinating material.