Formation of spin droplet at nu = 5/2 in an asymmetric quantum dot under quantum Hall conditions

TL;DR

This study investigates how geometric asymmetry in quantum dots influences the formation and properties of spin droplets at filling factor 5/2 under quantum Hall conditions, revealing significant effects on incompressibility and interference patterns.

Contribution

It introduces a self-consistent numerical approach to analyze asymmetric quantum dots and uncovers the impact of asymmetry on spin droplet formation and quantum interference phenomena.

Findings

Asymmetry significantly alters the incompressibility of the nu=5/2 state.

Electron distribution in Landau levels differs from symmetric quantum dots.

Asymmetry provides an additional parameter affecting Aharonov-Bohm oscillations.

Abstract

In this work, a quantum dot that is defined asymmetrically by electrostatic means induced on a GaAs/AlGaAs heterostructure is investigated to unravel the effect of geometric constrains on the formation of spin droplets under quantised Hall conditions. The incompressibility of exciting nu = 5/2 state is explored by solving the Schrodinger equation within spin density functional theory, where the confinement potential is obtained self-consistently utilising the Thomas-Fermi approximation. Our numerical investigations show that the spatial distribution of the nu = 2 incompressible strips and electron occupation in the second lowest Landau level considerably differ from the results of the laterally symmetric quantum dots. Our findings yield two important consequences, first the incompressibility of the intriguing nu = 5/2 state is strongly affected by the asymmetry, and second, since the Aharonov-Bohm interference patterns depend on the velocity of the particles, asymmetry yields an additional parameter to adjust the oscillation period, which imposes a boundary condition dependency in observing quasi-particle phases.