Screening theory based modeling of the quantum Hall based quasi-particle interferometers defined at quantum-dots

TL;DR

This paper models quantum Hall interferometers at quantum dots using screening theory, analyzing incompressible strips and interference conditions for fractional and integer quantum Hall states under magnetic fields.

Contribution

It introduces a microscopic, phenomenological model incorporating Laughlin quasi-particles and energy gaps to describe incompressible strips in quantum Hall interferometers.

Findings

Incompressible strips at bc=1/3 are characterized by an energy gap due to strong correlations.

Interference conditions depend on gate voltage, confinement potential steepness, and magnetic field strength.

The model provides insights into the spatial distribution and widths of edge states in quantum Hall regimes.

Abstract

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 \nu=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 \nu=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.