High temperature superconductors were discovered in 1986. The systems with the highest known transition temparatures become superconducting at around 135K (160K under pressure). The search for the theory of high Tc superconductivity is still one of the most hotly contested problems in condesed matter physics. The materials are complicated by many issues, one of which is the presence of strong electron-electron interaction effects and the existence of a transition between a Mott insulating antiferromagnet and a d-wave superconductor as a function of sample composition (or 'doping').

The research effort in our group has focussed on the nature of the superconducting state itself in these compounds. Here it is now established that the Cooper pairs have d-wave symmetry, rather than the usual s-wave symmetry known for almost all other superconductors. This tells us immediately that the pairing mechanism must be fundamentally different from conventional, or low Tc, superconductors where the famous Bardeen Cooper Schrieffer (BCS) theory applies. It also implies that the physical properties of the high Tc superconductors will be quite different from those of low Tc superconductors, for example they do not posess a true gap in the quasiparticle energy spectrum.  

The issue of unconventional pairing symmetry in superconductors has been the main focus of recent work in the group. The exotic material strontium ruthenate, Sr2RuO4, is a superconductor below 1.5K, and is believed to has spin triplet Cooper pairing. Work with G. Litak, K. Wysokinski and B. Gyorffy has focussed on the effect of spin-orbit coupling in aligning the orientation of the Cooper pair spins (pdf) . Another interesting spin-orbit coupling effect occurs in the heavy fermion superconductor CeSiPt3. This material has no centre of inversion symmetry, implying that both p and s wave pairing may exist simultaneously on its Fermi surface. I. Eremin and I have discovered that this leads to surprising changes in the superconducting gap node topology in an external magnetic field (pdf)  

The proximity effect between a conventional s-wave superconductor and a ferromagnetic material is the subject of another research project. The competition between the binding of opposite spin electrons into Cooper pairs and the ferromagnetic alignment of spins leads to a number of surprising effects. M. Krawiec, B. Gyorffy and I have predicted that the Andreev states at the interface may cause a spontaneous supercurrent to flow along the interface (pdf). This current turns out to be highly spin-polarised, and may have applications in the field of spintronics .  

The underlying theory of electronic structure of solids with strong correlation is another important topic of research. The usual band theory of solids is based upon approximations, such as the local density approximation (LDA) which are know to fail for strongly interacting systems, such as transition metal oxides, and d and f-band metals. For these materials we are working on developing more accurate, yet still first principles, approximations. Current research focusses on self-interaction correction (SIC), dynamical mean field theory (DMFT) and dynamical cluster approximation (DCA) approaches.