Fractional Quantum Hall States in Narrow Channels

TL;DR

This paper investigates the realization of fractional quantum Hall states in a confined 2D electron system under strong magnetic fields, using numerical methods to explore phase conditions and diagram.

Contribution

It demonstrates that fractional quantum Hall states can exist in narrow channels with harmonic confinement, providing a phase diagram for these states.

Findings

Fractional quantum Hall states are achievable in confined geometries.

A phase diagram for these states under different conditions is established.

Numerical diagonalization confirms the stability of these states in the model.

Abstract

A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical diagonalization of the Hamiltonian. It is shown that the fractional quantum Hall states are realized even in the presence of the external potential under suitable conditions, and a phase diagram is obtained.