Which topological order describes the 5/2 quantum Hall state? · revision history

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Revision 1: Which topological order describes the $5/2$ quantum Hall state
Revision 2: Which topological order describes the $5/2$ quantum Hall state?
Plain
Several candidate wavefunctions (named Pfaffian, anti-Pfaffian and particle-hole Pfaffian) predict different edge structures for the $5/2$ state, and experiments and computer simulations currently point to different answers.
Precise
For $\nu = 5/2$ in high-mobility GaAs quantum wells, determine the topological order. The thermal Hall conductance $\kappa_{xy} = c \kappa_0$, $\kappa_0 = \pi^2 k_B^2 T/(3h)$, distinguishes Pfaffian ($c = 7/2$), PH-Pfaffian ($c = 5/2$) and anti-Pfaffian ($c = 3/2$); the measured value is $5/2$ (Banerjee et al., 2018), while numerics with Landau-level mixing favour anti-Pfaffian or Pfaffian. An answer is an identification consistent with thermal Hall, upstream neutral modes, tunnelling exponents and numerics.
Settled by
Thermal Hall measurements with controlled edge equilibration, combined with numerics including realistic Landau-level mixing and disorder.
Kind
well-posed
Answer type
identification
References
(empty)
Literature status
contested
Status note
Experiments favour PH-Pfaffian (thermal Hall 2018; neutral-mode noise, Dutta et al. 2022; time-domain braiding noise consistent with PH-Pfaffian, arXiv:2608.12897, 2026), while numerics favour anti-Pfaffian or Pfaffian; proposed reconciliations (incomplete edge equilibration, domains, disorder-stabilized PH-Pfaffian) are debated as of 2026.
Posed since
(empty)

Decisions