The electron and current-density distributions in the close proximity of quantum point contacts ͑QPCs͒ are investigated. A three-dimensional Poisson equation is solved self-consistently to obtain the electron density and potential profile in the absence of an external magnetic field for gate and etching defined devices. We observe the surface charges and their apparent effect on the confinement potential, when considering the ͑deeply͒ etched QPCs. In the presence of an external magnetic field, we investigate the formation of the incompressible strips and their influence on the current distribution both in the linear response and out of linear response regime. A spatial asymmetry of the current carrying incompressible strips, induced by the large source drain voltages, is reported for such devices in the nonlinear regime.

In this work, we calculate the electron and the current density distributions both at the edges and the bulk of a two dimensional electron system, focusing on ideal and non-ideal contacts. A three dimensional Poisson equation is solved self-consistently to obtain the potential profile in the absence of an external magnetic field considering a Hall bar defined both by gates (contacts) and etching (lateral confinement). In the presence of a perpendicular magnetic field, we obtain the spatial distribution of the incompressible strips, taking into account the electron-electron interactions within the Thomas-Fermi approximation. Using a local version of Ohms law, together with a relevant conductivity model, we also calculate the current distribution. We observe that the incompressible strips can reside either on the edge or at the bulk depending on the field strength. Our numerical results show that, due to a density poor region just in front of the contacts, the incompressible strips do not penetrate to the injection region when considering non-ideal contact configuration. Such a non-ideal contact is in strong contrast with the conventional edge channel pictures, hence has a strong influence on transport. We also take into account heating effects in a phenomenological manner and propose a current injection mechanism from the compressible regions to the incompressible regions. The model presented here perfectly agrees with the local probe experiments all together with the formation of hot-spots.

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We report on our theoretical investigation of the effects of the confining potential profile and sample size on the electron velocity distribution in (narrow) quantum Hall systems. The electrostatic properties of the electron system are obtained by the Thomas-Fermi-Poisson nonlinear screening theory. The electron velocity distribution as a function of the lateral coordinate is obtained from the slope of the screened potential at the Fermi level and within the incompressible strips. We compare our findings with the recent experiments. © 2007 The American Physical Society

In this work, we calculate the current distribution, in the close vicinity of the quantum point contacts (QPCs), taking into account the Coulomb interaction. In the first step, we calculate the bare confinement potential of a generic QPC and, in the presence of a perpendicular magnetic field, obtain the positions of the incompressible edge states (IES) taking into account electron-electron interaction within the Thomas-Fermi theory of screening. Using a local version of the Ohm's law, together with a relevant conductivity model, we also calculate the current distribution. We observe that, the imposed external current is confined locally into the incompressible strips. Our calculations demonstrate that, the inclusion of the electron-electron interaction, strongly changes the general picture of the transport through the QPCs.

We report on our theoretical investigation of the electron velocity in (narrow) quantum-Hall systems, considering the out-of-linear-response regime. The electrostatic properties of the electron system are obtained by the Thomas-Fermi-Poisson nonlinear screening theory. The electron velocity distribution as a function of the lateral coordinate is obtained from the slope of the screened potential within the incompressible strips (ISs). The asymmetry induced by the imposed current on the ISs is investigated, as a function of the current intensity and impurity concentration. We find that the width of the IS on one side of the sample increases linearly with the intensity of the applied current and decreases with the impurity concentration.In the conventional models of the quantum Hall effect (QHE), the Coulomb interaction is ignored and either localization or the 1D edge states (ESs) was accepted as the explanation. However, recent experimental [1,2] and theoretical [3,4,5,6] investigations of the two dimensional electron systems (2DESs) under strong perpendicular magnetic fields B provided information about the

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.

We report on our theoretical investigation considering the widths of quantized Hall plateaus (QHPs) depending on the density asymmetry induced by the large current within the out-of-linear response regime. We solve the Schrödinger equation within the Hartree type mean field approximation using Thomas Fermi Poisson nonlinear screening theory. We observe that the two dimensional electron system splits into compressible and incompressible regions for certain magnetic field intervals, where the Hall resistance is quantized and the longitudinal resistance vanishes, if an external current is imposed. We found that the strong current imposed, induces an asymmetry on the IS width depending linearly on the current intensity.