William C. Hall
June 5, 2002
University of Arkansas at Little Rock

Summer 2002 Student Project Proposal

I will be working with Professor Lenore Horner, from Southern Illinois University at Edwardsville, on a research project related to the fractional Quantum Hall effect. Therefore, we have a 2-D electron system. In a 2-D system the electrons are confined to a quantum well where motion perpendicular to the sample surface is "frozen out,"since the excited states in that direction require a lot of energy. Specifically, we are interested in extended states, which cross the whole system from one end of the sample to the other. If the extended states exist, we want to know how many there are, what their size is, and how their size varies with their energy. These values will depend on the background potential (density of the peaks relative to the potential of the magnetic field, shape of the peaks, and randomness in the location of these peaks). We need to look at our data results, compare them to what other researchers have found, and determine what differences, if any, exist between our results and the results of others. Specifically, we will be looking at more types of systems than other researchers have. We will also investigate where the background potential is equivalent to a less that five percent filling factor. The long term goal of this project is to develop a unified theory of how the extended states behave throughout the range of systems. We feel that our theoretical results will add to the present understanding of how current and heat are conducted through various materials.