Fractional Quantum Hall Hierarchy and the Second Landau Level

TL;DR

This paper extends the fractional quantum Hall hierarchy to include non-Abelian states, specifically applying it to the second Landau level at nu=5/2, introducing new trial wavefunctions and a unifying pairing-based framework.

Contribution

It generalizes the hierarchy to non-Abelian states and constructs explicit trial wavefunctions for the second Landau level, unifying the understanding of observed Hall plateaus.

Findings

Reproduces all observed Hall conductance plateaus in the second Landau level.

Introduces explicit trial wavefunctions for the nu=5/2 state.

Highlights the role of electron pairing and non-Abelian anyons.

Abstract

We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.