We study the mean-field broken symmetry phases of charge neutral multilayer rhombohedral graphene within tight-binding approximations including self-consistent extended Hubbard interactions. We used onsite and intersite Hubbard interactions obtained from a newly developed first-principles calculation method. Our calculations for systems up to eight layers give rise to electron-hole asymmetries, band flatness, band gaps, and layer anti-ferromagnetic ground states in keeping with available experiments. By including the intersite Hubbard interactions up to the next-nearest neighboring sites, the band gaps are shown to open when the number of layers is larger than three, while the trilayer system maintains its metallic nature with two low energy density of state peaks near the Fermi energy whose separation increases with the range of intersite Hubbard parameters. Within our framework, the calculated band gaps reflect mean-field ground states with extended Hubbard interactions, in closer agreement with experimental estimates. The tight-binding formulation further enables efficient treatment of large rhombohedral chiral systems, including twisted multilayer graphene.

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• Electronic structure
• Graphene
• Extended Hubbard model
• Tight-binding model