We study the formation and characteristics of 'spin droplets', i.e. compact spin-polarized configurations in the highest occupied Landau level, in an etched quantum Hall device at filling factors 2 ≤ ν ≤ 3. The confining potential for electrons is obtained with self-consistent electrostatic calculations on a GaAs/AlGaAs heterostructure with experimental system parameters. Real-space spin-density-functional calculations for electrons confined in the obtained potential show the appearance of stable spin droplets at ν ~ 5/2. The qualitative features of the spin droplet are similar to those in idealized (parabolic) quantum-dot systems. The universal stability of the state against geometric deformations underlines the applicability of spin droplets in, for example, spin-transport through quantum point contacts.

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 ν = 5/2 state is explored by solving the Schrödinger 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 ν = 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 ν = 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.

In this work, we investigate the spatial distributions and the widths of the incompressible strips, i.e. the edgestates. The incompressible strips that correspond to ν = 1, 2 and 1/3 filling factors are examined in the presence of a strong perpendicular magnetic field. We present a microscopic picture of the fractional quantum Hall effect based interferometers, within a phenomenological model. We adopt Laughlin quasi-particle properties in our calculation scheme. In the fractional regime, the partially occupied lowest Landau level is assumed to form an energy gap due to strong correlations. Essentially by including this energy gap to our energy spectrum, we obtain the properties of the incompressible strips at ν = 1/3. The interference conditions are investigated as a function of the gate voltage and steepness of the confinement potential, together with the strength of the applied magnetic field.

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