The effects of Landau level mixing, finite thickness, and external electric fields on the $\nu=\frac{5}{2}$ fractional quantum Hall effect

The $\nu=\frac{5}{2}$ fractional quantum Hall effect (FQHE) is a unique and interesting experimental and theoretical state. A great deal of experimental, theoretical and numerical work suggests that this state may support quasihole excitations with non-Abelian statistics, where the order of particle exchange influences the final state of the system. Thus, the $\nu=\frac{5}{2}$ FQHE offers a system in which the properties of the particles may be explored experimentally and theoretically. Additionally, by controlling the exchange of such particles, it is possible to create a topologically-protected quantum computer. In order to make this possible, however, we must first understand the nature of the ground state. The two leading candidates, the Moore-Read Pfaffian and the anti-Pfaffian, both support non-Abelian excitations, but there has not been a clear answer for which state is realized in experiment. In the present work, we present results of exact diagaonlization calculations which strive to answer this question using a disk geometry. What we find is that the ground state of the system is dependent upon device specific quantities and thus we may be able to engineer samples which will have specific ground state properties.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics & Astronomy

Year

2015

Author dc:creator

• Tylan-Tyler, Anthony

Contributors dc:contributor

• Yuli Lyanda-Geller
• Erica Carlson
• Leonid Rokhinson
• Chris Greene

• fractional quantum Hall effect
• phase diagram
• spin-orbit coupled Bose-Einstein condensate

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/1433

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-2649