Universal Periods in Quantum Hall Droplets

TL;DR

This paper investigates the periodic behavior of quantum Hall droplets' ground states, proposing a model that aligns with experiments and predicts observable superperiods, aiding in understanding edge structures and neutral modes.

Contribution

It introduces a hierarchy-based model for quantum Hall droplets that explains periodic conductance variations and predicts superperiods in non-interfering geometries.

Findings

Model aligns with experimental observations

Predicts superperiods without interfering trajectories

Provides a method to detect neutral modes

Abstract

Using the hierarchy picture of the fractional quantum Hall effect, we study the the ground state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.