Moiré minibands in twisted homobilayer semiconductors can, under suitable approximations, be modeled as a pair of Landau levels with opposite Chern numbers. This provides a minimal model for searching novel topological states in a time-reversal-symmetric Hamiltonian. In this work, we investigate the effects of an external magnetic field in this model. We study the many-body ground state in the density–magnetic-field ($n\text{−}B$) plane along the $dn/dB=\pm 1/{\mathrm{\Phi }}_0$ Středa line with Hartree-Fock approximation. Away from charge neutrality, we find the Chern-insulating (incompressible) state is very robust while toward charge neutrality, we find a transition from incompressible phase to compressible phase as the interaction strength $\kappa$ decreases. Using time-dependent mean-field theory, we further analyze spin-flip excitations and find that the incompressible state along the Středa line toward charge neutrality becomes unstable even at large $\kappa$ when magnetic field is sufficiently large. Finally, we solve the two-body problem in a given Landau level exactly where the two particles experience unequal magnetic fields using a basis called center-of-charge basis. This basis allows any isotropic interaction to be parametrized by a single quantum number, the relative angular momentum, thereby extending the Haldane pseudopotentials to the unequal-magnetic-fields case. As the difference of the two magnetic fields varies, these pseudopotentials show a sequence of level crossings, leading to nonmonotonic structure of pseudopotentials that is absent in ordinary Landau-level systems. Our formulation provides a useful starting point for studying weak-field physics in moiré flat bands, where magnetic Bloch-state basis becomes computationally impossible due to the large basis sizes.

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• Chern insulators
• Flat bands
• Landau levels
• Moire materials
• Transition metal dichalcogenides
• Hartree-Fock methods