Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach

The complexity of the atomic-scale structures in twisted bilayer graphene (TBG) has made even the study of single-particle physics at low energies around the Fermi level challenging. We provide a convenient and physically motivated picture of single-particle physics in TBG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of ab initio tight-binding models, including the effects of atomic relaxations. We obtain for the first time the corresponding Wannier orbitals that incorporate all symmetries of TBG, which are also calculated as a function of angle, a requisite first step towards incorporating electron interaction effects. We construct eight-band and five-band models for the low-energy states for twist angles between 1.3° and 0.6°.