Anisotropy in the Compressible Quantum Hall State

TL;DR

This paper investigates anisotropic states in the quantum Hall system near half-integer filling factors using mean field theory, highlighting the stability and properties of unidirectional charge density waves.

Contribution

It introduces a self-consistent Hartree-Fock approach on the von Neumann lattice to analyze anisotropic compressible states and characterizes the UCDW as a collection of 1D lattice fermion systems.

Findings

UCDW is the most plausible state among anisotropic states.

The self-consistent Fermi surface of the 1D system is obtained.

Kinetic energy arises from Coulomb interactions.

Abstract

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around $\nu=l+1/2$ in the quantum Hall system. The Hartree-Fock energy of the UCDW are calculated self-consistently. In these states the unidirectional charge density wave (UCDW) seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermion systems which extend to the uniform direction. The kinetic energy of this one-dimensional system is induced from the Coulomb interaction term and the self-consistent Fermi surface is obtained.