A realistic quantum capacitance model for quantum Hall edge state based   Fabry-P\'{e}rot interferometers
  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. 
O. Kilicoglu, D. Eksi and A. Siddiki
cond-mat.mes-hall