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The enigmatic 12/5 fractional quantum Hall effect

We numerically study the fractional quantum Hall effect at filling factors $ν=12/5$ and 13/5 (the particle-hole conjugate of 12/5) in high-quality two-dimensional GaAs heterostructures via exact diagonalization including finite well width and Landau level mixing. We find that Landau level mixing suppresses $ν=13/5$ fractional quantum Hall effect relative to $ν=12/5$. By contrast, we find both $ν=2/5$ and (its particle-hole conjugate) $ν=3/5$ fractional quantum Hall effects in the lowest Landau level to be robust under Landau level mixing and finite well-width corrections. Our results provide a possible explanation for the experimental absence of the 13/5 fractional quantum Hall state as caused by Landau level mixing effects.