A triangular-lattice spin-valley Hubbard model in the ABC trilayer graphene/h-BN moire system

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This year there appear several amazing experiments  in the graphene moire superlattices.  In this talk I will focus on the ABC trilayer graphene/h-BN system. Mott-like  insulators at 1/4 and 1/2 of the valence band have already been reported by Feng Wang’s group at Berkeley. The sample is dual gated on top and bottom with voltage V_t and V_b.  V_t+V_b controls the density of electrons. Interestingly we find that the displacement field D=V_t-V_b can control both the topology and the bandwidth of the valence band. For one sign of D (for example D>0), there are two narrow Chern bands with opposite Chern numbers C=3,-3 for the two valleys. For D<0, the bands of the two valleys are trivial and have localized Wannier orbitals on a triangular lattice.  As a result, the physics is governed by a spin-valley Hubbard model on a triangular lattice. This talk focuses on the D<0 side and  consists of two parts:  (1) I will provide the details of this spin-valley Hubbard model and discuss some subtleties special to the moire systems.   (2) In the second part I want to show some of our theoretical attempts on this Hubbard model. First I will show that this system is a perfect platform for studying metal-insulating transition. I will provide a theory of continuous Mott transition between a Fermi liquid and a spinon Fermi surface Mott insulator. Second I will discuss some possible metallic phases upon doping away from the Mott insulator.  Unlike the familiar spin 1/2 case, the spin-valley Hubbard model may not be in a conventional Fermi liquid phase even in the over-doped region. I will provide some candidates of possible unconventional metals based on a six-flavor slave boson theory for the hole doped side.



Feng Wang et.al. arxiv: 1803.01985

Ya-Hui Zhang, Dan Mao, Yuan Cao, Pablo Jarillo-Herrero and T. Senthil.  arXiv:1805.08232

Ya-Hui Zhang and T. Senthil, arxiv: 1809.05110

Ya-Hui Zhang and T. Senthil, ongoing work