PIRSA:18100044

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

Zhang, Y. (2018). A triangular-lattice spin-valley Hubbard model in the ABC trilayer graphene/h-BN moire system. Perimeter Institute. https://pirsa.org/18100044

Zhang, Ya-Hui. A triangular-lattice spin-valley Hubbard model in the ABC trilayer graphene/h-BN moire system. Perimeter Institute, Oct. 30, 2018, https://pirsa.org/18100044 

          @misc{ pirsa_PIRSA:18100044,
            doi = {10.48660/18100044},
            url = {https://pirsa.org/18100044},
            author = {Zhang, Ya-Hui},
            keywords = {Condensed Matter},
            language = {en},
            title = {A triangular-lattice spin-valley Hubbard model in  the ABC trilayer graphene/h-BN moire system},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {oct},
            note = {PIRSA:18100044 see, \url{https://pirsa.org}}
          }

Ya-Hui Zhang

Massachusetts Institute of Technology (MIT)

Talk number
PIRSA:18100044
Collection
Talk Type
Subject
Abstract

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.

 

References:

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