Compressible Anisotropic States around the Half-Filled Landau Levels

TL;DR

This paper investigates the properties of anisotropic, compressible states near half-filled Landau levels in quantum Hall systems, highlighting the stability and characteristics of unidirectional charge density waves.

Contribution

It introduces a self-consistent calculation of the charge density profile and energy of the UCDW using the von Neumann lattice formalism, revealing its interpretation as a collection of 1D lattice Fermi-gas systems.

Findings

UCDW is the most plausible state near half-filled Landau levels.

The energy dependence on wave length of UCDW is numerically obtained.

The kinetic energy in UCDW arises dynamically from Coulomb interactions.

Abstract

Using the von Neumann lattice formalism, we study compressible anisotropic states around the half-filled Landau levels in the quantum Hall system. In these states the unidirectional charge density wave (UCDW) state seems to be the most plausible state. The charge density profile and Hartree-Fock energy of the UCDW are calculated self-consistently. The wave length dependence of the energy for the UCDW is also obtained numerically. We show that the UCDW is regarded as a collection of the one-dimensional lattice Fermi-gas systems which extend to the uniform direction. The kinetic energy of the gas system is generated dynamically from the Coulomb interaction.