Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems - Abstract
Friedland, Klaus-Jürgen
The self-rolling of thin, pseudomorphically strained semiconductor bilayer systems based on epitaxial heterojunctions grown by molecular-beam epitaxy allows to realize motion of electrons on curved surfaces. We realized a high-mobility, two-dimensional electron gas in which the low-temperature mean free path of the electrons is as large as the curvature radius of the tube, which allow us to study the interesting effects, in particular ballistic transport phenomena and the quantum Hall effect on a curved surface. The curvature of the surface results in a spatial change of the component of the magnetic field which is perpendicular to the surface, therefore, the filling factor changes gradually. For the quantum Hall effect we observe additional contributions in the longitudinal resistance. The phenomenon results from a specific current distribution in the quantized phase and can not be explained by the conventional Landauer--Büttiker approach which presupposes besides conductance along one-dimensional Landau channels a fully localized transport in the bulk. Moreover, we develop a model including the transport along incompressible stripes and the compressible (metallic) bulk. We also observe a new type of resistance oscillations in the ballistic transport of two-dimensional electrons on cylindrical surfaces with a tangentially directed magnetic field. The longitudinal resistance oscillates with a periodicity proportional to the square root of the magnetic field /B/, which indicates on a commensurability between the channel width and a length scale related to the gradient of the perpendicular to the surface component of the magnetic field. We show, that the lengths of a stripe with free electrons, forming the so called 'snake'-like trajectories is basic for the /square root B /oscillations. We speculate about a process, including spin procession of electrons in the one-dimensional 'skin'-channel forming around the /B /= 0 position, which causes this new type of resistance oscillations.