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

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

1999-12-29

arxiv.org/abs/cond-mat/9912479v2

Physical Review B, v. 61, pg. 16787 (2000)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

22 pgs. of PLAIN TeX, 1 fig. in postscript, published version

Scientific paper

10.1103/PhysRevB.61.16787

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.

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