The enigma of the $\nu=2+\frac{3}{8}$ fractional quantum Hall effect

TL;DR

This paper investigates the fractional quantum Hall state at ν=2+3/8, proposing it belongs to a new class of exotic non-Abelian states described by the Bonderson-Slingerland wave function, with testable predictions for its topological order.

Contribution

It identifies the ν=2+3/8 fractional quantum Hall state as a new exotic non-Abelian state with a complex wave function structure, expanding understanding of topological phases.

Findings

Suggests the state is described by Bonderson-Slingerland wave function

Predicts measurable quantities to confirm topological order

Links the state to non-Abelian anyons similar to Pfaffian at 5/2

Abstract

The fractional quantum Hall effect at $\nu=2+3/8$, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class of of exotic states described by the Bonderson-Slingerland wave function. Its excitations are non-Abelian anyons similar to those of the well studied Pfaffian state at 5/2, but its wave function has a more complex structure. Using the effective edge theory, we make predictions for various measurable quantities that should enable a confirmation of the underlying topological order of this state.