Possible Postgraduate Projects in Theoretical PhysicsNowadays there are a great many experiments which deal with nanoscale superconducting islands. Such superconducting granules can be manufactured by nanofabrication methods, and they have several possible applications, such as for 'Cooper pair boxes' which can be used in quantum computers. While such islands are small on macroscopic scales, they can still contain millions of atoms. Nevertheless the small sizes are approaching those which can be treated fully quantum mechanically in first principles calculations, such as Density Functional Theory (DFT). Modern numerical methods for DFT theory also include a full theory of superconductivity, which has proved highly successful in predicting properties of bulk materials. The new challenge in the project is to apply this theory to the case of a small superconducting island. Both the electrons and phonons are solved fully, and so this theory would be the first to make fully first-principles predictions of the effects of surfaces and the finite size effects on a real superconductor.
In the high temperature superconductors, such as YBa2CuO7, with critical temperatures of up to 90K and above, we now have a good understanding of the 'normal state' for 'overdoped' materials, i.e. ones with high numbers of conducting holes and we also have a good understanding of the 'd-wave' superconducting state. However on the 'underdoped' side of the phase diagram there is a strange region called the 'pseudogap phase'. This project will follow one possible interpretation of this phase, namely that it consists of a state where d-wave Cooper pairs have former, but where they have not yet Bose condensed into a d-wave superconducting state. These 'pre-formed pairs' are nearly localized on the copper-oxygen-copper bonds in the material, and can be modeled by a 'negative U' Hubbard Hamiltonian. We have already found that a static model of the random fluctuating phases of these Cooper pairs, leads to a good description of the strange 'Fermi-arcs' in this pseudogap phase. The project is to extend this work into the regime of dynamical fluctuations, so that we can for the first time fully address the interplay of localization and Bose Einstein condensation of these preformed Cooper pairs.
Frustrated magnets retain enormous spin-entropy at low temperatures, in apparent defiance of the zeroth law of thermodynamics. Where this entropy can be tuned using magnetic field, it offers a promising route to new magnetic refrigeration technologies. This project would use numerical and analytic methods to explore massive enhancement in cooling power seen near (quantum) critical points in frustrated ferromagnets.
The properties of electrons in one dimension are very strange and beautiful. However we live in a three-dimensional universe, and in real materials electrons are always able to explore a three dimensional space. None the less, there exist highly anisotropic, quasi one-dimensional metals which bear the imprint of one dimension. The goal of this project would be to provide theoretical support for ground-breaking transport experiments on quasi one-dimensional metals now being carried out in the correlated electron system group in Bristol.
CMR systems contain both local moments and itinerant electrons, and are of technological interest because spin and charge properties are strongly interdependent. However at present, their electronic properties are usually discussed at the level of a band structure or mean field theory for a clean system. This project would explore the role of disorder and quantum fluctuations on the electronic properties of CMR materials using Feynman diagrams, with the goal of gaining a better understanding of experiment.
This is not an exclusive list and other projects will be available shortly from Dr M R Dennis. Anyone interested in Quantum Information, which is a discipline with collaborations over three departments should also apply to the School of Mathematics.
Information on how to apply can be found on the Postgraduate Admissions page.
General enquiries should be addressed to Tracie Anderson.