Current distribution in narrow translation-invariant quantum-Hall-systems with lateral density modulation

Abstract

A previously developed self-consistent screening and magneto-transport theory for laterally confined, translation-invariant quantum-Hall-systems is applied to two-dimensional electron systems created by a donor sheet with a lateral density modulation. The previous calculations, assuming a homogeneous donor charge density, could explain experimental results on the spatial distribution of an applied source-drain-current, and the resulting Hall potential, only for the 'edge-dominated' low-magnetic-field part of a quantum-Hall-plateau, where the current flows through incompressible stripes near the edges. For the high-magnetic-field regime of the plateau, they predicted current flow only in a narrow stripe in the center of the sample, whereas the experiments found current in a wide region of its bulk. Assuming a suitably modulated donor charge density, we can avoid this discrepancy, and we obtain a strong dependence of the distribution of the applied current on magnetic field, lattice temperature, and the current-strength.

Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect

“…The cusp-structure seen in the logarithmic plot of (lowest panel of Figure 8) results from the fact, that the number of ISs in the system changes at these -values. These results are consistent with those obtained for the modulation with and [40].…”

“…The resistance results for a modulated system, Eq. (13) with and , have also been published [40] and are consistent with those shown in Figure 8, which shows the linear response resistance for the models with described in Figure 5. Figure 8 shows Hall and longitudinal resistance as a function of the magnetic field for two temperatures and for two donor-density modulations with the indicated parameters (red lines) and (green lines).…”

“…The calculations for Figure 15 have been performed without modulation of the donor chargedensity and without a spatial average of electron density and conductivity. Calculations with such spatial averages and without modulation as well as with modulation [40] of the donor density have also been performed and yielded qualitatively very similar results. In Figure 15 a -value in the high-region of the ( )-QHP is considered, and therefore in the not-quantized dissipative states is larger than (see e.g., Figure 8).…”

“…This changes drastically as is lowered further. At K the conductivity components and in the broad IS near are well quantized, most of the ASDC flows with nearly constant current density and constant Hall field through this stripe and the increase of the local electron temperature is very small, , by orders of magnitude smaller than at [40]. These drastic changes with temperature will, of course, lead to strong variations of the global resistance components, which will be discussed in the following sections.…”

“…In order to describe such situations, a model with a modulated donor density has been considered. cos (13) Some results for cm , and have been published some time ago [39], and some for cm , and more recently [40]. For these models the electron densities at and , calculated from the linear integral equation 9with ∫ cos (14) are plotted in Figure 5.…”