Intervalley coherence, vortex lattice and fractional quantum spin Hall effect in moiré MoTe2

Recent experiments have demonstrated the presence of the Fractional Quantum Spin Hall Effect in moiré MoTe₂ at a twist angle of 2.1 degrees and filling factor of 3. We investigate the system with a model with adiabatic approximation, which maps the two valley's Chern bands to Landau levels. Due to the opposite signs of the Chern numbers, the effective magnetic fields in the two valleys are also opposite. Applying the Hartree-Fock approximation, we find that the ground state can be intervalley coherent. These coherent states exhibit an Abrikosov-like vortex lattice pattern in real space and show zero Hall conductivity, consistent with experimental observations.