Compressible anisotropic states around the half-filled Landau levels

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 wavelength 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.