Localized Excitons and Landau-Level Mixing in Time-Reversal Symmetric Pairs of Chern Bands

Abstract

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 ($V^{\uparrow \uparrow }$) and opposite-spin ($V^{\uparrow \downarrow }$). Using degenerate perturbation theory, we compute Landau-level mixing corrections to $V^{\uparrow \uparrow }$ and $V^{\uparrow \downarrow }$ for different filling fractions. In the lowest Landau level, screening exhibits an even-odd effect: $V^{\uparrow \uparrow }$ is reduced more strongly than $V^{\uparrow \downarrow }$ 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 $V^{\uparrow \downarrow }$ is reduced comparably to $V^{\uparrow \uparrow }$, 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 time-reversal-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 MoTe${}_2$ on the Landau-level mixing parameter.

28 pages, 6 figures, comments are welcome