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.
@article{arxiv.1604.04610,
title = {The enigmatic 12/5 fractional quantum Hall effect},
author = {Kiryl Pakrouski and Matthias Troyer and Yang-Le Wu and Sankar Das Sarma and Michael R. Peterson},
journal= {arXiv preprint arXiv:1604.04610},
year = {2016}
}