Determine the topological orders of the two field-induced ν = 3/2 FQH phases

Determine the topological character of the soft-gap and hard-gap fractional quantum Hall states at filling factor ν = 3/2 induced by an in-plane magnetic field, including whether the two phases realize distinct topological orders.

Background

The experiment identifies successive transitions at ν = 3/2 from a composite-fermion liquid to a soft-gap fractional quantum Hall state and then to a hard-gap robust fractional quantum Hall state. The observed gap closure at the second transition suggests a topological phase transition, but transport measurements and the observed daughter state at ν = 19/13 do not uniquely distinguish among candidate orders such as anti-Pfaffian and anti-(331).

The authors present several tentative mechanisms, including anyon condensation, a transition associated with splitting of the Fermi contour into two components, and paired composite-fermion states. They explicitly leave the topological identification of both phases unresolved and call for further theoretical and numerical work.