We predict resistance anomalies to be observed at high mobility two dimensional electron systems (2DESs) in the fractional quantized Hall regime, where the narrow (L <10 ?m) Hall bar is defined by top gates. An analytic calculation scheme is used to describe the formation of integral and fractional incompressible strips. We incorporate the screening properties of the 2DES, together with the effects of perpendicular magnetic field, to calculate the effective widths of the current carrying channels. The many-body effects are included to our calculation scheme through the energy gap obtained from the well accepted formulation of the composite fermions. We show that, the fractional incompressible strips at the edges, assuming different filling factors, become evanescent and co-exist at certain magnetic field intervals yielding an overshoot at the Hall resistance. Similar to that of the integral quantized Hall effect. We also provide a mechanism to explain the absence of 1/3 state at the Fabry-Perot interference experiments. Yet, an un-investigated sample design is proposed to observe and enhance the fragile effects like interference and overshooting based on our analytical model.
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 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 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 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.
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. 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.
The electrostatic screening of a medium disordered quantum Hall liquid was investigated using an electric field penetration (EFP) technique. At sufficiently low temperatures and at magnetic fields corresponding to the integral quantum Hall regime with even filling factors, two topologically different phases of the bulk electron liquid have been identified. By means of elementary analysis of experimental data it has further been shown that the transition between these phases reveals features typical of a Kosterlitz–Thouless type phase transition. Finally, the validity of the presented physical picture has been supported by means of numerical simulations of local filling factor topography.
In this work, we exploit the findings of the screening theory of the integer quantized Hall effect (QHE) based on the formation of the incompressible strips and its essential influence on the global resistances and propose certain experimental conditions to observe the bulk to edge transition of the QHE in a phenomenological model. We propose a Hall bar design on a cleaved edge overgrown wafer, which allows us to manipulate the edge potential profile from smooth to extremely sharp. For a particular sample design and by the help of a side gate perpendicular to the two dimensional electron system (2DES), it is shown that the plateau widths can be changed and even made to vanish when changing the edge potential profile. Such a control of the edge potential implies peculiar transport results when considering the screening theory, which includes direct Coulomb interaction explicitly. We think that, these experiments will shed new light on the understanding of the QHE.
We present experimental results where hysteresis is observed depending on the magnetic field sweep direction in the integer quantum Hall regime of a high-mobility two-dimensional electron system formed in a GaAs/AlGaAs heterostructure. We analyze the results based on the screening theory and show that the anomalous effects observed stem from the nonequilibrium processes resulting from the formation of metal-like and insulator-like regions due to direct Coulomb interactions and the dissipative nature of the Hall bar together with the scattering-influenced contacts. Furthermore, the hysteretic behavior is shown for the integer filling factors $\ensuremath{\nu}=1$, 2, and 4 and for certain fractional states at the longitudinal resistance. We argue that the nonequilibration is not only due to contacts, in contrast, but also due to the nature of the finite size dissipative Hall bar under interactions and Landau quantization.
Experimental and theoretical investigations on the integer quantized Hall effect in gate-defined narrow Hall bars are presented. At low electron mobility the classical (high-temperature) Hall resistance line RH(B) cuts through the center of all Hall plateaus. In contrast, for our high-mobility samples the intersection point, at even filling factors ν=2, 4, ..., is clearly shifted towards larger magnetic fields B. This asymmetry is in good agreement with predictions of the screening theory, i.e. taking Coulomb interaction into account. The observed effect is directly related to the formation of incompressible strips in the Hall bar. The spin-split plateau at ν=1 is found to be almost symmetric regardless of the mobility. We explain this within the so-called effective g-model.
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