Microscopic theory of the activated behavior of the quantized Hall effect

The thermally activated behavior of the gate defined narrow Hall bars is studied by analyzing the existence of the incompressible strips within a Hartree-type approximation. We perform self-consistent calculations considering the linear response regime, supported by a local conductivity model. We investigate the variation of the activation energy depending on the width of samples in the range of $2d\sim [1-10] \mu m$. We show that the largest activation energy of high-mobility narrow samples, is at the low field edge of Hall filling factor 2 plateau (exceeding half of the cyclotron energy), whereas for relatively wide samples the higher activation energy is obtained at the high field edge of Hall plateau. In contrast to the single-particle theories based on the localization of electronic states, we found that the activation energy is almost independent of the properties of the density of states.Comment: 8 pages, 4 figure

Quantum Hall Resistance Overshoot in 2-Dimensional Electron Gases - Theory and Experiment

We present a systematical experimental investigation of an unusual transport phenomenon observed in two dimensional electron gases in Si/SiGe heterostructures under integer quantum Hall effect (IQHE) conditions. This phenomenon emerges under specific experimental conditions and in different material systems. It is commonly referred to as Hall resistance overshoot, however, lacks a consistent explanation so far. Based on our experimental findings we are able to develop a model that accounts for all of our observations in the framework of a screening theory for the IQHE. Within this model the origin of the overshoot is attributed to a transport regime where current is confined to co-existing evanescent incompressible strips of different filling factors.Comment: 26 pages, 10 figure

Interaction mediated asymmetries of the quantized Hall effect

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 \nu = 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 \nu= 1 is found to be almost symmetric regardless of the mobility. We explain this within the so-called effective g-model.Comment: 4 pages, 3 figure

The visibility of IQHE at sharp edges: Experimental proposals based on interactions and edge electrostatics

The influence of the incompressible strips on the integer quantized Hall effect (IQHE) is investigated, considering a cleaved-edge overgrown (CEO) sample as an experimentally realizable sharp edge system. We propose a set of experiments to clarify the distinction between the large-sample limit when bulk disorder defines the IQHE plateau width and the small-sample limit smaller than the disorder correlation length, when self-consistent edge electrostatics define the IQHE plateau width. The large-sample or bulk QH regime is described by the usual localization picture, whereas the small-sample or edge regime is discussed within the compressible/incompressible strips picture, known as the screening theory of QH edges. Utilizing the unusually sharp edge profiles of the CEO samples, a Hall bar design is proposed to manipulate the edge potential profile from smooth to extremely sharp. By making use of a side-gate perpendicular to the two dimensional electron system, it is shown that the plateau widths can be changed or even eliminated altogether. Hence, the visibility of IQHE is strongly influenced when adjusting the edge potential profile and/or changing the dc current direction under high currents in the non-linear transport regime. As a second investigation, we consider two different types of ohmic contacts, namely highly transmitting (ideal) and highly reflecting (non-ideal) contacts. We show that if the injection contacts are non-ideal, however still ohmic, it is possible to measure directly the non-quantized transport taking place at the bulk of the CEO samples. The results of the experiments we propose will clarify the influence of the edge potential profile and the quality of the contacts, under quantized Hall conditions.Comment: Substantially revised version of manuscript arXiv:0906.3796v1, including new figures et