At filling ν=1, intervalley-coherent states in opposite-Chern Landau level models are ground states only for reduced intravalley interactions, and their gapless spin mode rules them out as the sole explanation of the fractional quantum spin Hall effect.
Haldane, A modular-invariant modified weierstrass sigma-function as a building block for lowest-landau-level wavefunctions on the torus, Journal of Mathematical Physics59(2018)
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Valley Order in Moir\'e Topological Insulators
At filling ν=1, intervalley-coherent states in opposite-Chern Landau level models are ground states only for reduced intravalley interactions, and their gapless spin mode rules them out as the sole explanation of the fractional quantum spin Hall effect.