This thesis scrutinizes the condensed matter physics phenomenon known as the fractional quantum Hall effect (FQHE), in particular fractional quantum Hall effects occurring in multicomponent systems. Broadly speaking, the FQHE can be defined as a many-electron quantum phenomenon, driven by strong interactions, that occurs in two-dimensional electron gasses in the presence of a perpendicular external magnetic field (and it is also predicted to occur for any two-dimensional particles, such as confined cold atoms, in an external gauge field). Multicomponent systems are systems where the constituent particles (such as electrons or cold atoms) possess internal degrees of freedom, for instance a spin or valley index. These internal degrees of freedom are often overlooked when modeling the FQHE. Taking into account the multicomponent degree of freedom yields an abundance of possibilities for the intellection of new types of so-called “topological phases of matter”, which are ubiquitously associated with the FQHE. In this thesis several different cases are considered. The first topic discussed herein is a study of phase transitions that can take place between FQHE phases with different net values of their multicomponent degrees of freedom. Examples are phase transitions between phases of different uniform net spin polarization, tunable as a function of certain system parameters. Some significant technical refinements are made to a previous model and comparisons are made with a variety of different experiments. The results are relevant for multicomponent FQHEs occurring in GaAs,AlAs and SiGe semiconductor systems where the electronic structure is confined to two dimensions, as well as in two-dimensional materials such as graphene. The second topic discussed herein is the introduction of the multiparticle multicomponent pseudopotential formalism. This methodology is oriented towards considerably expanding an existing framework for the construction of exactly solvable FQHE models by parameterizing multicomponent interactions. The final topic is the first example application of this new formalism to the construction of an exactly solvable FQHE model.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:606348 |
| Date | January 2013 |
| Creators | Davenport, Simon C. |
| Contributors | Simon, Steven H. |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:6a907943-c134-4986-93bc-30766a424b9c |
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