Stability of the compressible quantum Hall state around the half-filled Landau level

TL;DR

This paper investigates the stability of compressible quantum Hall states near half-filling using mean field theory, revealing conditions under which these states become unstable or remain stable based on system parameters.

Contribution

It introduces a mean field approach on the von Neumann lattice to analyze the stability of compressible states in the quantum Hall system near half-filling.

Findings

Compressibility becomes negative below a critical spacer width d.

The state is unstable at filling factor ν=1/2.

Stable compressible states exist around ν=1/2 above the critical d.

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 $\nu$ 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 $\nu=1/2$. Within a finite range around $\nu=1/2$, the stable compressible state exists above the critical value of $d$.