Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases

TL;DR

This paper analyzes the edge modes of fractional quantum Hall states, including cases with negative flux, providing explicit wavefunctions and describing both Abelian and non-Abelian edge structures with counterpropagating modes.

Contribution

It introduces explicit trial wavefunctions for edge modes in fractional quantum Hall states with negative flux, including non-Abelian cases, and clarifies their structure and propagation.

Findings

Edge modes can be explicitly constructed from effective theories.

Negative flux leads to counterpropagating edge modes.

Wavefunctions for specific filling factors are provided.

Abstract

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general quantum Hall states have many edge states. Here we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve in all cases explicit derivative operators diminishing the angular momentum of the system.