Magneto-Transport Study of Disordered Electron Systems in a Gallium Arsenide Heterojunction.

A systematic transport study of the role of disorder in the quantum Hall effect is presented. The device used for this study is a disorder-tuned two-dimensional electron gas in a Gallium Arsenide-Aluminum Gallium Arsenide heterostructure, and the measurements were taken at ultra-low temperatures, down to 50 mK. When deeply in the variable-range hopping regime, this system has a giant negative magnetoresistance at low magnetic fields, where reduction of the resistance with application of magnetic field can be as large as a factor of 15. It is shown that this effect is orbital in origin. The crossover from negative to positive magnetoresistance was found to occur at complete filling of the lowest spin -unresolved Landau level, i.e., when nu = 2. The Hall coefficient was also studied. For vanishing temperature in the Anderson insulating regime, the sample is characterized by vanishing longitudinal and transverse conductivities and diverging longitudinal resistivity, but the transverse resistivity remains finite and equal to its classical value. Hence, the density found from the classical Hall coefficient is not a measure of extended carriers. A system exhibiting this type of behavior was termed a Hall insulator. A transition from an Anderson insulator at low and high magnetic fields to a quantum Hall liquid in the intermediate region of nu = 2 was observed. For vanishing temperature the longitudinal resistivity diverges in insulating regime and the longitudinal resistivity vanishes in the quantum Hall liquid regime. While in quantum Hall liquid regime the sample is characterized by a well-defined Hall plateau of value h/2e^2 A comparison to the global phase diagram is made. The positions of the extended states in the density-magnetic field plane have been investigated. Strong upward deviation of the delocalized states from their traditional Landau level positions at low magnetic fields was seen. An analysis of this result is given in terms of the so called "floating" equation.