Floating extended states in a disordered quantum Hall system

Several recent experiments, on various GaAs systems, have shown that an insulating phase at B = 0 can undergo a phase transition to the quantum Hall liquid (QHL) phase in an applied magnetic field B. The transition was generally interpreted as being consistent with the global phase diagram (GPD) of the quantum Hall effect. While the GPD is parametrized in terms of disorder and magnetic field, another canonical theory treats the field-induced delocalization phenomenon in the context of "floating" energy levels. While the two theories are not inconsistent with each other, this thesis will present experimental evidence in direct support for the latter theory. it will be demonstrated conclusively that it is indeed the levitation (or floating) of a delocalized state (as B {dollar}to{dollar} 0) that underlies the delocalization transition.; A complete understanding of the remarkable phenomenon clearly requires a reasonable microscopic picture. Toward this end, two recent theoretical papers have suggested that Landau level mixing is at the root of the experimentally observed levitation. In fact, it has already been shown numerically that the energy of the delocalized states can shift upward due to Landau level mixing. Experimentally, a similar determination, with respect to Landau level mixing, necessitates the examination of the density of states (DOS). In order to obtain the relevant DOS information, we have conducted a systematic study of the minimum conductivity in the vicinity of the insulator-quantum Hall liquid transition. Since, at low-temperatures, hopping between localized sates is the dominant conduction mechanism for a QHL state, the minimum in conductivity should directly reflect the minimum in the DOS. Experimental evidence will be presented, through an anomalous behavior of the conductivity minimum, that Landau level mixing is indeed important and directly associated with the floating of the delocalized states.