The enigmatic 12/5 fractional quantum Hall effect

TL;DR

This study uses numerical methods to investigate the fractional quantum Hall effect at specific filling factors, revealing how Landau level mixing influences the stability of these states in GaAs heterostructures.

Contribution

It demonstrates that Landau level mixing suppresses the 13/5 fractional quantum Hall effect, explaining its experimental absence, while showing the robustness of 12/5, 2/5, and 3/5 states.

Findings

Landau level mixing suppresses the 13/5 state

12/5, 2/5, and 3/5 states remain robust

Provides explanation for experimental observations

Abstract

We numerically study the fractional quantum Hall effect at filling factors $\nu=12/5$ 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 $\nu=13/5$ fractional quantum Hall effect relative to $\nu=12/5$. By contrast, we find both $\nu=2/5$ and (its particle-hole conjugate) $\nu=3/5$ 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.