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, the edge physics of an Aharonov-Bohm interferometer (ABI) defined on a two dimensional electron gas, subject to strong perpendicular magnetic field B, is investigated. We solve the three dimensional Poisson equation using numerical techniques starting from the crystal growth parameters and surface image of the sample. The potential profiles of etched and gate defined geometries are compared and it is found that the etching yields a steeper landscape. The spatial distribution of the incompressible strips is investigated as a function of the gate voltage and applied magnetic field, where the imposed current is confined to. AB interference is investigated due to scattering processes between two incompressible "edge-states".

A numerical approach is employed to explain transport characteristics in realistic, quantum Hall-based Aharonov-Bohm (AB) interferometers. Firstly, the spatial distribution of incompressible strips, and thus the current channels, are obtained by applying a self-consistent Thomas-Fermi method to a realistic heterostructure under quantized Hall conditions. Secondly, the timedependent Schrödinger equation is solved for electrons injected in the current channels. Distinctive AB oscillations are found as a function of the magnetic flux. The oscillation amplitude strongly depends on the mutual distance between the transport channels and on their width. At an optimal distance the amplitude and thus the interchannel transport is maximized, which determines the maximum visibility condition. On the other hand, the transport is fully suppressed at magnetic fields corresponding to half-integer flux quanta. The results confirm the applicability of realistic AB interferometers as controllable current switches. Recent low-temperature transport experiments [3-8] performed at two-dimensional (2D) electron systems (2DESs) utilize the quantum Hall (QH) effect to investigate and control the electron dynamics via their AB phase. An interesting difference between the original AB experiments and QH interferometers is the fact that in the latter the electron path itself may depend on the magnetic field B. To describe electron transport in QH interferometers, the singleparticle edge-state approach [9] is common, but neglects the dependence of the area enclosed by the current-carrying channels on the magnetic field [10], as well as on the channel widths. However, as shown explicitly below, the actual paths can be obtained considering the full manybody electrostatics, which yields the spatial distribution of compressible and incompressible strips [11].The essential features of the observed AB oscillations in QH interferometers have been explained using edge-channel simulations and Coulomb interactions at the classical (Hartree) level [4,12,13]. However, a complete theoretical picture of the observed phenomenon is still missing [6,14]. To attain this, it would be particularly important to (i) describe the full electrostatics by handling the crystal growth parameters and the 'edge' definition of the interferometer and (ii) supply this scheme with a dynamical study on electronic transport in the 2DES.The objective of this work is to take important steps towards a comprehensive explanation of the AB characteristics in QH interferometers. Firstly, we apply the 3D Poisson equation and the Thomas-Fermi approximation to the given heterostructure [15], taking into account the lithographically defined surface patterns. In this way, we obtain the electron and potential distributions under QH conditions [16,17]. For completeness, we utilize this scheme for the real experimental geometry resulting from the trench-gating technique. Secondly, we determine a model potential describing the current channels and use a time-dependent propagation scheme to mon...

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

The effect of an electric field on the non-hydrogenic binding energy of a shallow donor impurity in a cylindrical cross-sectional GaAs-(Ga,Al)As quantum well wire (QWW) was investigated. Within the effective mass approximation, the non-hydrogenic binding energy of the donor impurity was calculated by a variational method as a function of the wire radius, donor impurity position and applied electric field. The results show that the non-hydrogenic binding energy of the donor impurity located around the centre is larger than that of the hydrogenic binding energy. The difference in binding energy of an on-centre shallow donor impurity in the two regimes increases more rapidly with decreasing QWW radius than for other impurity positions. It has been found that the sensitivity of the donor binding energies to the applied electric field in both regimes is almost the same.