<p> A two-dimensional electron system exposed to a strong perpendicular magnetic field at low temperatures (usually below one Kelvin) forms a new state of matter that exhibits the fractional quantum Hall effect. This phenomenon has been observed in graphene, a naturally occurring two-dimensional electron system. The theoretical understanding of the FQHE in graphene is complicated by the fact the electrons have valley and spin degrees of freedom. As a result, the different single-particle energy levels (Landau levels) of the electrons can mix with each other. This Landau level mixing is intrinsic to graphene and must be considered in any realistic theoretical treatment. Recently, an effective model Hamiltonian which includes Landau level mixing has been formulated in terms of Haldane pseudopotentials: this model includes emergent three-body interactions in addition to renormalizing the two-body interactions. We construct an effective real-space two-body interaction potential using a closed form expression found in the literature that can model various realistic effects including Landau level mixing. Our method will allow us to fully tackle the physics of the fractional quantum Hall effect in graphene and provide a method for extending our studies to realistic models of semiconductor heterostructure systems as well.</p><p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10636101 |
| Date | 05 December 2017 |
| Creators | Getachew, Yonas |
| Publisher | California State University, Long Beach |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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