@phdthesis{Siddiki2005,
  author    = {Siddiki, Afif},
  title     = {Model calculations of current and density distributions in dissipative Hall bars},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-15100},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {In this work we examine within the self-consistent Thomas-Fermi-Poisson approach the low-temperature screening properties of a two-dimensional electron gas (2DEG) subjected to strong perpendicular magnetic fields. In chapter 3, numerical results for the unconfined 2DEG are compared with those for a simplified Hall-bar geometry realized by two different confinement models. It is shown that in the strongly nonlinear-screening limit of zero temperature the total variation of the screened potential is related by simple analytical expressions to the amplitude of an applied harmonic modulation potential and to the strength of the magnetic field. In chapter 4 we study the current and charge distribution in a two-dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasilocal transport model, that includes nonlinear screening effects on the conductivity via the self-consistently calculated density profile. The existence of "incompressible strips" with integer Landau level filling factor is investigated within a Hartree-type approximation, and nonlocal effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the longitudinal resistance as continuous functions of the magnetic field B, with plateaus of finite widths and the well-known, exactly quantized values. We emphasize the close relation between these plateaus and the existence of incompressible strips, and we show that for B values within these plateaus the potential variation across the Hall bar is very different from that for B values between adjacent plateaus, in agreement with recent experiments. We have improved on the previous chapter by a critical investigation of the impurity potential profiles and obtained reasonable estimates of the range and the amplitude of the potential fluctuations. We added a harmonic perturbation potential to the confining potential in order to generate the long-range-part of the overall impurity potential in the translation invariant model. This treatment of the long-range fluctuations allowed us to resolve apparent discrepancies such as the dependence of the QH plateau width on the mobility and to understand the crossing values of the high and low temperature Hall resistances. An interesting outcome of this model is that, it predicts different crossing values depending on the sample width and mobility. In chapter 6 we brie y report on theoretical and experimental investigations of a novel hysteresis effect that has been observed on the magneto-resistance (MR) of quantum-Hall (QH) bilayer systems in magnetic field (B) intervals, in which one layer is in a QH-plateau while the other is near an edge of a QH-plateau. We extend a recent approach to the QH effect, based on the Thomas-Fermi-Poisson theory and a local conductivity model to the bilayer system. This approach yields very different density and potential landscapes for the B-values at different edges of a QH plateau. Combining this with the knowledge about extremely long relaxation times to the thermodynamic equilibrium within the plateau regime, we simulate the hysteresis in the "active" current-carrying layer by freezing-in the electron density in the other, "passive", layer at the profile corresponding to the low-B edge of its QH plateau as B is swept up, and to the profile at the high-B edge as B is swept down. The calculated MR hysteresis is in good qualitative agreement with the experiment. If we use the equilibrium density profile, we obtain excellent agreement with an "equilibrium" measurement, in which the system was heated up to ~ 10K and cooled down again at each sweep step.},
  subject      = {Elektronengas},
  language  = {en}
}