In this thesis we investigate a system of three tunnel-coupled quantum dots, arranged in a triangular geometry and attached to a single metallic conduction band, using both analytic and semi-analytic methods and the numerical renormalisation group technique. This is the simplest coupled quantum dot system to exhibit frustration. We study three different models of the triple quantum dot device: a mirror symmetric arrangement of dots in which only one dot is connected to the conduction band, a triple quantum dot system in which only one dot is connected to the conduction band without a plane of mirror symmetry and a mirror symmetric arrangement of quantum dots in which all three dots are coupled to the conduction band. We study these models over a wide range of parameter space, and in both the presence and absence of a magnetic field. Both antiferromagnetic and ferromagnetic Kondo effects are observed, and in all three models we find that the system contains at least two phases, and so a number of quantum phase transitions may be observed, associated in some cases with significant changes in the low temperature conductance through the triple quantum dot device. In addition to zero-field Kondo physics, a number of field induced Kondo effects are also observed. Both first order quantum phase transitions and Kosterlitz-Thouless phase transitions are observed. We use both symmetry arguments and low energy effective models which we derive to explain and understand both the position of and type of phase boundary that is observed in each case, and perturbative methods are used to accurately predict Kondo temperatures for a wide range of systems.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:572522 |
| Date | January 2012 |
| Creators | Jarrold, Thomas Furnley |
| Contributors | Logan, David E. |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:e2772c4e-6c76-44b8-9c02-401d9f90b27f |
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