Wigner crystal state for the edge electrons in the quantum Hall effect at fillingν=2

Abstract

The electronic excitations at the edges of a Hall bar not much wider than a few magnetic lengths are studied theoretically at filling ν = 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.