The crossover transport regime between the quantum Hall effect and the Aharonov-Bohm effect is studied in terms of Buttiker's approach of electrical conduction. Quantum Hall effect and Aharonov-Bohm effect are very important effects in mesoscopic physics and both demonstrate unambiguously that quantum mechanics is the dominant factor in nanoscale electrical transport problems. However, they belong to situations of different dimensionality and different strength of magnetic fields. Our goal is to reveal the physics at the crossover regime between the two and find the transport properties of this transition regime. / We have computed Hall resistance of a four-probe box-shaped quantum dot with an artificial impurity confined inside. As the size of the impurity is increased, transport behavior changes from the usual quantum Hall regime to a regime dominated by strong Aharonov-Bohm (AB) oscillations. We observe directly the formation and coupling of the edge states and their effects on the Hall resistance, by varying a magnetic field. For a range of the impurity size, transport enters the crossover regime where quantum Hall and AB effects compete, and a peculiar approximate symmetry between various transmission coefficients lead to a Hall plateau before the quantum Hall regime is reached. This symmetry can be explained based on scattering matrix theory and a topological equivalence of the dominating transmission patterns where well defined edge states are formed. Finally we investigate the universality of the observed symmetry property in several other structures and find that within the scope of our calculation the symmetry is universal.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.23910 |
| Date | January 1996 |
| Creators | Lei, Ming |
| Contributors | Guo, Hong (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001499621, proquestno: MM12224, Theses scanned by UMI/ProQuest. |
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