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 > or = 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 q(3/2) like 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.

Pinning Modes of the Stripe Phases of 2d Electron Systems in Higher Landau Levels

“…For ν between 4.40 and 4.60, the hard-and easy-direction spectra are strikingly different, with a resonance around 100 MHz only in the hard-direction conductivity, Re(σ xx ). This range of ν is in good agreement with theoretical predictions [12][13][14][15][16] for the presence of the stripe phase.…”

Wigner crystal and bubble phases in graphene in the quantum Hall regime

“…15,16 We call these states anisotropic Wigner crystals, and the ones having a triangular or square lattice structure as isotropic Wigner crystals.…”

Variational Monte Carlo calculation of the nematic state of the two-dimensional electron gas in a magnetic field

“…For the stripe-ordered state, the optimum energy is obtained by minimizing the energy with respect to the uniaxial anisotropy parameter defined in Ref. 23. Figure 7 shows the comparison of the optimal energies obtained by MC for the nematic state with the optimum ͑with respect to ͒ energy for the stripe state obtained by HF.…”

“…͑v͒ The optimum value of ␣ is determined by minimizing the total energy. ͑vi͒ The HF results, which have been reported so far, [21][22][23] correspond to the case of = 0. Therefore, we needed to carry out HF calculations following Refs 21-23 for the case of the interaction given by Eq.…”