Flat-band projected versus fully atomistic twisted bilayer graphene

We benchmark the recently proposed projection method [Phys. Rev. B 111, 205133 (2025)] for magic-angle twisted bilayer graphene (MATBG) across various symmetry-breaking phases at charge neutrality. The flat-band projected solutions agree well with the full tight-binding, with band structures and total energies differing by only a few meV. The projection to the flat bands is justified, owing to the increased gap to the remote bands in the normal state. Moreover, we employ a novel set of order parameters that allow us to visualize the wave functions locally in real space and quantify the breaking of various symmetries in the correlated phases. These order parameters are suitable for characterizing MATBG and generic honeycomb systems.

💡 Research Summary

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This paper presents a comprehensive benchmark of the recently proposed flat‑band projection method (Phys. Rev. B 111, 205133 (2025)) against a fully atomistic tight‑binding (TB) Hartree‑Fock calculation for magic‑angle twisted bilayer graphene (MATBG). The authors focus on charge‑neutrality and examine a set of experimentally relevant symmetry‑breaking phases: the symmetric normal state (SYM), nematic semimetal (NSM), quantum anomalous Hall (QAH), Kramers intervalley coherent (KIVC), orbital‑polarized (OP), time‑reversal intervalley coherent (TIVC), and valley‑polarized (VP) states.

Model and Computational Details
A realistic TB Hamiltonian is built using Slater‑Koster parameters for the π‑orbitals, with a twist angle of 1.05° that yields a moiré supercell containing 11 908 carbon atoms. Atomic relaxation follows the model of Ref.