Extended Data Fig. 4: Hartree-Fock bands and real-space wavefunction calculations.

a, Non-interacting single particle band structure for tMoTe₂ with a twist angle of 2.45°. b, Hartree-Fock band structure with spin-split bands for a small interaction strength of ε = 60. The Fock energy is inhomogeneous across momentum space, resulting in momentum dependent gaps across the Brillouin zone. It is noteworthy that the first moiré Chern band is fully gapped out, but the second Chern band remains gapless, consistent with transport measurements of a weak metallic state at ν = -3. c, Real-space hole density of the first (ρ₁) and second (ρ₂) Chern bands calculated for 2.45° twisted MoTe₂. Both ρ₁ and ρ₂ form a honeycomb lattice at the MX and XM sites, leading to ferromagnetism via direct exchange. d, e, Wavefunction distribution across the moiré unit cell for the first Chern band at the γ point (d) and κ/κ′ point (e). Both form a honeycomb lattice, consistent with the hole density distribution in c. f, g, Wavefunction distribution for the second Chern band at the γ point (f) and κ/κ′ point (g). The wavefunctions are normalized with respect to their maximum value within the moiré unit cell. In contrast to the κ/κ′ point, which remains a honeycomb lattice, the γ point forms a triangular lattice which has decreased mean-field Fock energy. As a result, the gap between the two spin-split Chern bands in (b) is less for the γ point compared to the κ/κ′ point. h, i, j, Wannier orbitals for each valley (spin) localized at the MX, XM and MM site, respectively.