Wigner Crystal State for the Edge Electrons in the Quantum Hall Effect at Filling $\nu = 2$

TL;DR

This paper investigates the edge electron states in quantum Hall systems at filling factor 2, proposing a stable antiferromagnetic Wigner-crystal ground state that explains different theoretical predictions.

Contribution

It introduces a unified antiferromagnetic Wigner-crystal model for edge electrons at filling factor 2, reconciling mean-field and Luttinger liquid theory results.

Findings

Stable spin-density wave state along the edge.

Dominant Wigner-crystal correlations predicted.

Zeeman splitting causes canting of the antiferromagnetic order.

Abstract

The electronic excitations at the edges of a Hall bar not much wider than a few magnetic lengths are studied theoretically at filling $\nu = 2$. Both mean-field theory and Luttinger liquid theory techniques are employed for the case of a null Zeeman energy splitting. The first calculation yields a stable spin-density wave state along the bar, while the second one predicts dominant Wigner-crystal correlations along the edges of the bar. We propose an antiferromagnetic Wigner-crystal groundstate for the edge electrons that reconciles the two results. A net Zeeman splitting is found to produce canting of the antiferromagnetic order.