A realistic quantum capacitance model for quantum Hall edge state based Fabry-P\'{e}rot interferometers

TL;DR

This paper develops a realistic quantum capacitance model for Fabry-Pérot interferometers in the quantum Hall regime, combining self-consistent electrostatic and quantum calculations to analyze conductance oscillations.

Contribution

It introduces a comprehensive model that integrates classical and quantum capacitances with self-consistent simulations for realistic geometries.

Findings

Conductance oscillations depend on sample properties beyond size.

Both Aharonov-Bohm and Coulomb Blockade effects can explain conductance oscillations.

Modeling helps distinguish the origins of observed oscillations.

Abstract

In this work, the classical and the quantum capacitances are calculated for a Fabry-P\'{e}rot interferometer operating in the integer quantized Hall regime. We first consider a rotationally symmetric electrostatic confinement potential and obtain the widths and the spatial distribution of the insulating (incompressible) circular strips using a charge density profile stemming from self-consistent calculations. Modelling the electrical circuit of capacitors composed of metallic gates and incompressible/compressible strips, we investigate the conditions to observe Aharonov-Bohm (quantum mechanical phase dependent) and Coulomb Blockade (capacitive coupling dependent) effects reflected in conductance oscillations. In a last step, we solve the Schr\"odinger and the Poisson equations self-consistently in a numerical manner taking into account realistic experimental geometries. We find that, describing the conductance oscillations either by Aharanov-Bohm or Coulomb Blockade strongly depends on sample properties also other than size, therefore, determining the origin of these oscillations requires further experimental and theoretical investigation.