A realistic quantum capacitance model for quantum Hall edge state based Fabry–Pérot interferometers

Abstract

Abstract.In this work, the classical and the quantum capacitances are calculated for a FabryPérot 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 Schrödinger 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.

The topological inequivalence of Hall bar versus Corbino geometries in real space

“…An explicit expression capacitance is not given in the paper, however, is suggested by himself to be a quantum capacitance, 45 which is directly connected to the compressibility of the system. 46 In the following subsection, we introduce the fundamental formalism to calculate self-consistently both the electron and current density distributions assuming periodic boundary conditions in both directions, within the Thomas-Fermi approximation (TFA) that assumes that the potential varies smoothly on quantum mechanical length scales.…”

Investigating the current distribution of parallel-configured quantum point contacts under quantum Hall conditions

“…Starting with these boundary conditions, one obtains V (x, y, z) and ρ(x, y, z) depending on the potential on gates, strength of doping and thickness of GaAs and AlGaAs layers. Equipped with the self-consistently calculated potential and charge density distributions for each layer at zero temperature and magnetic field, one can obtain the density and current distributions in the presence of external in-plane electric and off-plane magnetic fields, using the Newton-Raphson iteration [14][15][16]. Our strategy is to use V (x, y, z) as an initial input, obtained in the previous step, and calculate finite temperature and magnetic field reconstructed potential and charge distributions.…”

“…At 10 Tesla magnetic energy, ωc( ωc = eB/m * ) is on the order of 17 meV, and thermal energy (T ≤ 10 K) is much smaller than the confinement energy (approximately 4 eV) and potential (energy) on metallic gates (∼ -0.2 eV). The details of the calculation procedures and validity of the assumptions are explained in our previous studies [8,16].…”