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

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