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.
|Advisor:||Peterson, Michael R.|
|Commitee:||Bill, Andreas, Gredig, Thomas|
|School:||California State University, Long Beach|
|Department:||Physics and Astronomy|
|School Location:||United States -- California|
|Source:||MAI 57/01M(E), Masters Abstracts International|
|Subjects:||Physics, Condensed matter physics|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be