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

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 constraints on the formation of spin droplets under quantized Hall conditions. The incompressibility of the excited nu = 5/2 state is explored by solving the Schr odinger equation within spin density functional theory, where the confinement potential is obtained self-consistently utilizing 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 quasiparticle phases.