Anisotropic states of two-dimensional electrons in high magnetic fields

TL;DR

This paper investigates the anisotropic stripe states of two-dimensional electrons in high magnetic fields near half-filling, revealing their structure, elastic properties, and collective excitations through self-consistent Hartree-Fock calculations.

Contribution

It introduces a detailed analysis of the stripe state as an anisotropic Wigner crystal and computes its elastic properties, clarifying the nature of its collective modes.

Findings

Stripe state is an anisotropic Wigner crystal.

Shear modulus is small but finite within HF approximation.

Magnetophonon mode vanishes as q^{3/2} at long wavelengths.

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.