Topological order of even-denominator states in bilayer graphene
In plain words
Bilayer graphene shows several half-integer quantum Hall states with larger energy gaps than the gallium arsenide $5/2$ state, and which non-Abelian order each one has is not settled.
Precise statement
For even-denominator states in Bernal bilayer graphene (half-integer fillings such as $-1/2, 3/2\text{ and }7/2$ in $N = 1$ orbital levels), determine the topological order (Pfaffian, anti-Pfaffian or other) of each, including its dependence on displacement field and orbital or valley polarization. An answer gives $\kappa_{xy}$ and quasiparticle charge per state, consistent with numerics.
What would settle it
Thermal Hall and tunnelling-exponent measurements per state, combined with exact diagonalization including Landau-level mixing.
Status in the literature
Unverified note
Interferometry since 2024 reports e/4 and e/2 signals (arXiv:2412.19886); no thermal Hall measurement is known to this survey as of 2026.