Anisotropic states of two-dimensional electrons in high magnetic fields

Abstract

We study the collective states formed by two-dimensional electrons in Landau levels of index $n\ge 2$ near half-filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes like $q^{3/2}$ as in an ordinary Wigner crystal, and not like $q^{5/2}$ as was found in previous studies where the energy of shear deformations was neglected.

minor corrections; 5 pages, 4 figures; version to be published in Physical Review Letters

References in corpus (1)

• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels

Cited by in corpus (9)

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• Pinning mode resonances of 2D electron stripe phases: Effect of in-plane magnetic field
• Fluctuations and topological transitions of quantum Hall stripes: nematics as anisotropic hexatics
• Variational Monte-Carlo calculation of the nematic state of the two-dimensional electron gas in a magnetic field
• Dynamical matrix of two-dimensional electron crystals
• The microscopic picture of the integer quantum Hall regime