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.

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

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Cited by in corpus (13)

• Wigner crystal and bubble phases in graphene in the quantum Hall regime
• Quantum nematic as ground state of a two-dimensional electron gas in a magnetic field
• Observation of pinning mode of stripe phases of 2D systems in high Landau levels
• Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling
• Pinning mode resonances of 2D electron stripe phases: Effect of in-plane magnetic field
• Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
• Microscopic details of stripes and bubbles in the quantum Hall regime
• RD-NMR spectra of the crystal states of the two-dimensional electron gas in a quantizing magnetic field
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Fluctuations and topological transitions of quantum Hall stripes: nematics as anisotropic hexatics
• Dynamical matrix of two-dimensional electron crystals
• Variational Monte-Carlo calculation of the nematic state of the two-dimensional electron gas in a magnetic field
• The microscopic picture of the integer quantum Hall regime