Bridging Hubbard Model Physics and Quantum Hall Physics in ABC Trilayer Graphene/h-BN moir\'e superlattice

Recently several phases resulting from electron correlations have been discovered in graphene moire superlattice with narrow bands. In this talk I will focus on the moire superlattice formed by ABC stacked trilayer graphene aligned with a hexagonal boron nitride substrate (TG/h-BN). Mott-like insulators in this system have already been observed experimentally by Feng Wang et.al. (Chen, Feng Wang et.al. arxiv: 1803.01985). Remarkably, in TG/h-BN, both the bandwidth and the topology can be tuned by an applied perpendicular electric field D . For D<0, the valence bands of the two valleys are trivial and the physics is governed by a spin-valley Hubbard model on triangular lattice. For D>0, the bands of the two valleys have non-zero Chern numbers C=3,-3. Therefore the TG/h-BN system can simulate both Hubbard model physics and nearly flat Chern band physics within one sample through a simple switch of the vertical displacement field. I am going to discuss several aspects of the resulting many body physics.