Interacting Twisted Bilayer Graphene with Systematic Modeling of Structural Relaxation

Tianyu Kong, Alexander B. Watson, Mitchell Luskin, Kevin D. Stubbs

We introduce and compute solutions of a many-body model of the electronic properties of twisted bilayer graphene which systematically accounts for the effects of structural relaxation. We model mechanical relaxation by coupling linear elasticity to a stacking energy that penalizes disregistry. Minimizers of the resulting functional are then input into a tight-binding model of twisted bilayer graphene, from which a single-particle continuum moiré-scale (Bistritzer-MacDonald-like) model is systematically derived. We then project this model together with a Coulomb electron-electron interaction term into the single-particle model’s flat moiré bands. We numerically compute Hartree-Fock ground states of this model, comparing the relative energies of competing many-body ground states.

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