Physics Graduate Student Seminar with Joseph Roseph Cruise on The quantum hall effect: anyons for anyone

Despite our knowledge that the world is comprised entirely of quantum mechanical particles, traditional intuition suggests that statistical systems of these quantum degrees of freedom can be described by classical theories with no quantized observables. It was then quite a shock when, in 1980, Klaus Von Klitzing observed near perfect quantization of the hall resistance in a sample of silicone MOSFET at certain ranges of large magnetic fields. The explanation to this mysterious quantization has revolutionized theoretical condensed matter physics and has crucial implications in the study of topological insulators, non-abelian anyons, topological quantum field theory, topological quantum computing, and more. My talk aims to review the basic development of the integer and fractional quantum hall effects, so that I can offer some insight into the origin of the quantization of the hall resistance. No background knowledge in condensed matter physics is required.