Localized Excitons and Landau-Level Mixing in twisted MoTe₂

We study Landau-level mixing in a time-reversal–symmetric Hamiltonian composed of two sets of Landau levels with opposite magnetic field, relevant to moiré minibands in twisted homobilayer transition-metal dichalcogenides in the adiabatic limit, where electrons in opposite valleys have flat Chern bands with opposite Chern numbers. Strong spin–orbit coupling polarizes spins in opposite directions in opposite valleys, separating Coulomb interactions into like-spin (V_↑↑) and opposite-spin (V_↑↓). Using degenerate perturbation theory, we compute Landau-level mixing corrections to V_↑↑ and V_↑↓ for different filling fractions. In the lowest Landau level, screening exhibits an even–odd effect: V_↑↑ is reduced more strongly than V_↑↓ in even-m angular momentum Haldane pseudopotential and less strongly in odd-m angular momentum ones. In the first Landau level, the short-range part (m = 0, 1) of V_↑↓ is reduced comparably to V_↑↑, while the strongest spin anisotropy appears in the m = 2 pseudopotential. These novel short-range spin correlations have important implications for candidate correlated phases of fractional quantum spin Hall insulators. A distinctive feature of this timereversal–symmetric Hamiltonian, absent in conventional quantum Hall systems, is that spin-flip excitations form localized quasiparticles. We compute their excitation spectrum and predict a non-monotonic dependence of the ordering temperature of Chern ferromagnetism in MoTe₂ on the Landau-level mixing parameter.