Ground-state identification at the STM displacement-field point

Determine whether the ground state at the STM experimental point S+—corresponding to the N=2 Landau level of bilayer graphene at B_perp=13.95 T and an interlayer potential difference U=30 meV—is the composite-fermion Fermi liquid or the Moore–Read state.

Background

The paper calculates a phase diagram for the competition between the composite-fermion Fermi liquid, the Moore–Read state, and stripe phases in the half-filled N=2 Landau level of bilayer graphene. The point S+ represents the parameters of an STM experiment that observed an even-denominator fractional quantum Hall state.

At S+, the calculated energies of the composite-fermion Fermi liquid and Moore–Read state are too close to distinguish within the numerical uncertainties. The authors therefore identify only a trend toward Moore–Read stabilization at larger displacement fields, leaving the phase at the experimental point unresolved.

References

Unfortunately, in our computation, we could not resolve the nature of the ground state at $S_{+}$, as the energies of both the CFFL and MR states are very close, and their difference is comparable to the error bars.

— 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 4.1, paragraph following Fig. 5