Trial wavefunction for fractional quantum spin Hall insulator

We propose a trial wavefunction for a fractional quantum spin Hall state (FQSH) in systems with conjugate Chern bands, motivated by recent experimental advances in twisted transition metal dichalcogenides. Our construction begins with two conjugate copies of the Moore-Read Pfaffian states for two spin species and introduces a coupling between their neutral fermionic excitations, forming an "anyonic exciton" that condenses. The resulting trial state represents a Z_4 FQSH insulator. The anyonic exciton condensation leads to a variational wavefunction characterized by intra-spin p-wave and inter-spin s-wave pairing of the composite fermions. We analyze the energetics of this wavefunction using variational Monte Carlo simulations. We identify the interaction regimes that can favor this trial Z_4 FQSH state. Our approach provides a new method for understanding incompressible FQSH states in conjugate Chern band systems.