Abstract
We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.
Highlights
The recent discovery of the superconductivity and strongly correlated insulating state in the twisted bilayer graphene (TBG) [1,2] has attracted enormous attention and triggered a surge of theoretical works on this subject [3,4,5,6,7,8,9,10,11,12,13,14,15,16]
We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene
At the filling of two electrons per supercell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which could possibly lead to an unconventional many-body state
Summary
The recent discovery of the superconductivity and strongly correlated insulating state in the twisted bilayer graphene (TBG) [1,2] has attracted enormous attention and triggered a surge of theoretical works on this subject [3,4,5,6,7,8,9,10,11,12,13,14,15,16]. The nearly flat bands are separated by the energy gaps from other bands [1,37,38], making it possible to construct an effective lattice model with well-localized Wannier orbitals purely consisting of the flat band states. Such an effective model was predicted by the symmetry analysis [4], which concludes that the Wannier orbitals should be centered at nonequivalent AB and BA spots in the moirepattern, to form an emergent honeycomb lattice. By taking an appropriate linear combination of the Bloch states in the nearly flat bands, we build the Wannier orbitals centered at the AB and BA spots and obtain the effective tight-binding model on the emergent honeycomb lattice.
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