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This is an experimental thesis, intended to discover new features of the Fractional Quantum Hall Effect (FQHE), by the fabrication of lithographic microstructures. It begins with an exposition of the theory required to understand electrical transport in Gallium Arsenide high mobility semiconductor heterostructures at low temperatures, and high magnetic fields. It continues with the various theories which attempt to explain the origin of the FQHE, and some predictions that have been made. The role of fractionally-charged quasiparticles is discussed, particularly with reference to the Aharonov-Bohm effect (AB). Experimental measurements are presented of the Aharonov-Bohm effect in the FQHE, and analysis is presented as to their interpretation. Numerical models are shown to describe the energy dependence of the Aharonov-Bohm oscillations, and fitted to experiment. There is a discussion of how the Fermi liquid model of the edge states in the FQHE produces different predictions than the Luttinger liquid model, and the Fermi liquid model is shown to give a good fit to the experimental data. The edge of the sample in the FQHE is currently a subject of much discussion, so this thesis presents results about the equilibration of electronic edge states in the FQHE. An experimental device was developed which allows a continuous variation in the slope of the electrostatic potential at the edge, thus allowing the equilibration to be altered. Scattering coefficients between edge states, both in the integer and fractional Quantum Hall regimes are derived, and the implications discussed, as is the energy dependence of the scattering, for which a theory is developed. Novel oscillations in the scattering coefficients are also observed, and the system is used to experimentally refute the theoretical prediction that under certain circumstances quasiparticles propagate counter to the standard direction. |
