Nature of the 2/5 state at the second-Landau-level point

Determine the topological nature of the ν=2/5 fractional quantum Hall ground state at the n=1 Landau-level point by resolving the competition among the Jain, anti-Read–Rezayi 3-cluster, and Bonderson–Slingerland candidate states.

Background

At filling ν=2/5, the paper compares the Abelian Jain state with the non-Abelian anti-Read–Rezayi 3-cluster and Bonderson–Slingerland states as the effective interaction is tuned through the N=2 Landau level of bilayer graphene.

The n=1 Landau-level interaction is known to favor a state distinct from the Jain state, but the numerical phase diagram does not resolve which of the competing non-Abelian candidates is lowest in energy at that point.

References

Unfortunately, we could not fully resolve the nature of the ground state at the $n{=}1$ LL point in our phase diagram.

— Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the $\mathcal{N}{=}2$ Landau levels of Bernal-stacked bilayer graphene  (2609.19379 - Dora et al., 16 Sep 2026) in Section 4.5, final paragraph