Short Versus Long Range Exchange Interactions in Twisted Bilayer Graphene

This study discusses the effect of long‐range interactions within the self‐consistent Hartree‐Fock (HF) approximation in comparison to short‐range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, it determines the quasi‐particle band structure of TBG with Hubbard interactions for three magnetic orderings: modulated anti‐ferromagnetic (MAFM), (NAFM) and hexagonal anti‐ferromagnetic (HAFM). Then, it develops an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, it observes a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, the HF potential plays a major role in the band structure, with HAFM and MAFM being secondary effects, but NAFM appears to still significantly distort the electronic structure at the magic angle. These findings suggest that the spin‐valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favor magnetic order, since the atomistic Hubbard interaction will break this symmetry in favor of spin polarization. The work presented in the manuscript studies the combined effect of long and short‐range interactions in twisted bilayer graphene. The rich phase diagram of this system is expected to arise from the interplay between these interactions. The results show that long and short‐range interactions describe the main effects of the phase diagram at different angles, with long range interactions being the dominant coupling at small angles, while short‐ range interactions dominate at large angles. The calculations are carried out by combining continuum and atomistic models. This approach paves the route toward large scale calculations that will simultaneously consider atomic scale and moiré scale effects.