Stability of the Compressible Quantum Hall State around the Half-Filled Landau Level

Abstract

We study the compressible states in the quantum Hall system using a mean field theory on the von Neumann lattice. In the lowest Landau level, a kinetic energy is generated dynamically from Coulomb interaction. The compressibility of the state is calculated as a function of the filling factor $\ensuremath{\nu}$ and the width $d$ of the spacer between the charge carrier layer and dopants. The compressibility becomes negative below a critical value of $d$ and the state becomes unstable at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$. Within a finite range around $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$, the stable compressible state exists above the critical value of $d$.