The Stability of the Quantum Hall State at $\nu = 1$ in Bilayer Electron Systems

TL;DR

This study investigates the stability of the quantum Hall state at filling factor $ u=1$ in bilayer electron systems using density functional theory, highlighting conditions for stability and effects of impurities.

Contribution

It provides a phase diagram for the transition to the quantum Hall state in double quantum dots and analyzes the impact of impurity potentials on its stability.

Findings

Quantum Hall state can be stable at zero tunnel splitting.

Impurity potential influences the stability conditions.

Phase diagram of the transition at $ u=1$ was constructed.

Abstract

The ground states of electrons in two vertically coupled quantum dots in the presence of an external magnetic field have been studied within the density functional theory. A phase diagram of the transition to the quantum Hall state in double quantum dots has been plotted for the Landau level filling factor $\nu = 1$. It has been shown that the quantum Hall state can be stable for a zero tunnel splitting. The influence of the impurity potential on the stability condition for the quantum Hall state has been analyzed.