Theory of flat bands, correlated insulators and superconductivity in graphene Moire heterostructures

The remarkable discovery of correlated insulating behavior and superconductivity in twisted bilayer graphene (TBG) inspired a vast theoretical and experiment effort to (i) understand the origin of this behavior including the nature of symmetry breaking and the mechanism of the superconducitivity and (ii) find similar systems which share some of its interesting properties while differing in some details leading to a wider range of possible phases. The purpose of this talk is to present some recent works contributing to the progress on these two fronts. In regards to (i), we will present an exhaustive discussion of possible mean field symmetry broken states in TBG [1]. By highlighting the existence of a hidden approximate symmetry in the model, we will identify a manifold of low-energy states whose competition is settled by small symmetry breaking terms and present numerical results supporting this argument. Furthermore, we will discuss their possible experimental signatures and comment on their compatibility with different experiments. Regarding (ii), we will discuss a related Moire system, twisted double bilayer graphene (TDB), which was recently synthesized experimentally [2] and shown to exhibit correlated insulating behavior and spin-triplet superconductivity. We will show the results of a thorough analysis of its band structure, correlated insulating state and superconducting phase which compare favorably with experimental findings [3].


[1] S. Liu, E. Khalaf, J. Y. Lee, and A. Vishwanath, arXiv:1905.07409 (2019) and in preparation with Bultinck, Chatterjee, Liu, Vishwanath and Zaletel.
[2] X. Liu, Z. Hao, E. Khalaf, J. Y. Lee, K.Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, arXiv:1903.08130 (2019)
[3] J. Y. Lee, E. Khalaf, S. Liu, X. Liu, Z. Hao, P. Kim, and A. Vishwanath, arXiv:1903.08685 (2019)