Charge Ordering in Twisted Bilayer Graphene Modeled by a Hubbard-like Hamiltonian, Supplemented with Long-range Density–Density Interactions

Moiré systems, such as twisted bilayer graphene or coupled layers of transition metal dichalcogenides, are considered intriguing platforms for understanding a variety of phenomena observed in strongly correlated electron systems. Here, we apply the four-band lattice model of twisted bilayer graphene to analyze whether, in the undoped case, the range of density–density interactions influences the resultant charge ordering. By using semi-classical simulated annealing optimization, as well as unrestricted Hartree–Fock calculations, we show that the pattern of order clearly depends on the range of interaction terms assumed; by performing the energy scaling with the increasing range of interactions taken into account, we select two patterns that possibly refer to the optimal charge distribution at doping \(ν =0\) — that is, at charge neutrality in the real system. Abstract Published by the Jagiellonian University 2026 authors