Correlated insulating states and broken symmetries in magic angle twisted bilayer graphene

Magic angle twisted bilayer graphene exhibits insulating and superconducting behaviors when its low energy flat bands are partially filled[1]. Insulating states have been seen near all integer band filling factors, which strongly suggests that they are associated with states that break spin/valley flavor but not translational symmetries. I will first present our understanding of the nature of the insulating states[1] based partially on self-consistent Hartree-Fock (SCHF) calculations, which show that the insulating states can be understood qualitatively in terms of broken symmetries that gap the continuum model’s Dirac points as the twist angle is approached[2] from above and the Dirac velocities approach zero. Remote conduction and valence bands play an important quantitative role. Screening of Coulomb interactions due to the response of the metallic gates weakens Coulomb interactions, and can among other effects enlarge the stability region of superconducting states. Away from integer filling the bilayer system is metallic. I will argue on the basis of recent experiments that spin/valley flavor symmetries are often broken even in metallic and superconducting states and extend our SCHF calculations to metallic cases in an effort to shed light on electronic properties in the metallic regime. I will also discuss our recent effort using exact diagonalization method calculations based on a continuum-model defined low energy Hilbert space, which confirm some of the main results obtained using SCHF and point to some limitations. The exact diagonalization calculations suggest that Coulomb interaction alone are not enough to yield Cooper pairing, and that phonon induced effect attractive interactions have to be included in order to have a Cooper instability.
[1]X. Lu, et al., Nature 574, 653–657(2019)
[2]M. Xie and A. H. MacDonald, arXiv:1812.04213.