Possible Postgraduate Projects in Theoretical Physics

Professor J F Annett and Prof B.L. Gyorffy:  Spin-orbit coupling in de Hass van Alphen measurements

In the de Haas van Alphen effect a large magnetic field is used to measure the shape and size of the Fermi surface. The original theory of Lars Onsager beautifully showed that oscillations in manetization in a metal occur periodically with 1/B (where B  is the magnetic field), and the frequency depends on the extremes in cross sectional area of the Fermi surface, S, in a plane perpendicular to the field. Although the theory is well established, the effects of spin-orbit coupling on this result are not well understood. For example recent advances in understanding of spin-orbit effects in materials have been shown to lead to corrections to the usual semi-classical transport theory of metals, such as those used in Onsager's theory. Non-trivial geometric  (Berry) phases occur leading to new phenomena such as the anomalous Hall effect. This project is to investigate whether these Berry phase contributions may also make a similar contribution to the de Haas van Aphlen effect, extending the previous semi-classical analysis of Duncan and Gyorffy[1].  For example we may study these effects in the unconventional superconductor Sr₂RuO₄, where spin-orbit effects are already known to have a significant effect on the de Haas van Alphen measurements of the Fermi surface[2].

[1]  A damping of the de Haas-van Alphen oscillations in the superconducting state, Duncan KP and Gyorffy BL J. Phys.-Condens. Matter  15   239-247   (2003)
Times Cited: 2 (from All Databases)

 [2] : Spin-orbit coupling and k-dependent Zeeman splitting in strontium ruthenate, Rozbicki Emil J.; Annett James F.; Souquet Jean-Rene and Mackenzie, Andrew P, J. Phys.-Condens. Matter 23   Issue: 9   094201   (2011).

Professor J F Annett:  Cooper pairs above T_c in a d-wave 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.

Dr Mark Dennis:  Please contact Mark Dennis directly for possible PhD project ideas for 2012 entry.

Prof J. Hannay:  Please contact Prof Hannay directly for possible PhD project ideas for 2012 entry.

Prof S. Popescu :  Please contact Prof Popescu directly for possible PhD project ideas for 21012 entry.

Anyone interested in Quantum Information, which is a discipline with collaborations over several 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 James Annett.