New Physics at the Interface Between the Classical and Quantum Worlds

Condensed matter physics is an area of both technological and fundamental scientific importance. Modern technology isincreasingly dependent upon the quantum behaviour of matter on the smallest scale. The race to make a quantumcomputer seeks to use this behaviour very directly, but quantum mechanics is important in more familiar technology:transistors, superconductors and the read heads in hard drives all depend crucially upon the quantum mechanics ofelectrons in solids.Understanding the collective quantum behaviour of electrons in solids is not only an important driver of technology, but italso raises fundamental issues with impact in other areas of science. To take a topical example, the explanation of whysuperconductors hover in magnetic fields (the Meissner effect) was provided by the Anderson-Higgs mechanism --- thevery same mechanism that is now thought to provide the origin of mass itself and which is currently being investigated atFERMILAB the LHC in CERN.There is a tremendous symbiosis between theory and experiment in condensed matter physics. New theoretical ideas arecrucial in guiding experiment in fruitful directions and puzzling results from experiment are essential in aiding thedevelopment of theory --- unraveling these puzzles can lead to fundamental principles that have an impact much furtherafield.I study the theory of the collective quantum behaviour of electrons. I develop mathematical theories predicting neweffects not yet seen in experiment and work with experimentalists to understand how these new effects can be observed.Together, we determine which experimental anomalies might be understood within current theories. Those that cannotprovide important guidance and new directions for theoretical investigation.Much of my time is spent studying quantum critical systems. These systems are balanced between the quantum andclassical worlds --- they obey rules that are partly like the classical rules of everyday experience and partly the strangequantum rules of the very smallest scale. A large variety of materials have electronic behaviour that is quantum critical.They have a property that physicists call universality: their behaviour at low energy and long distances is largelyindependent of the high energy and short distance behaviour. Because of this, they provide a forum in which we canunderstand general features of how classical world emerges from the quantum behaviour on the microscopic scalewithout being distracted by details such as differences between materials.

Profile: This proposal has the potential to generate fundamental advances that will inevitably enhance the profile of UK science. The UK has a world-leading effort in experiments on quantum critical systems, coordinated through programmes such as the EPSRC Portfolio Partnership Novel Quantum Order in Interacting Electron Metals . My programme aims to bring a similar visibility to UK theoretical efforts. The use of recently installed grid infrastructure promises to be a cost-effective new way of coordinating research across the UK. The enhanced interactions between theory and experiment that result will give tremendous leverage to research and will provide training for graduate students and post-doctoral researchers that is of greater relevance to industry. The scientific results of this research will advertise the breadth and quality of the UK skills base. Skills Base: a) Post-doctoral Fellows (PDRAs): The immediate training benefit would be felt by the PDRAs. My programme will afford them the opportunity to develop both cutting edge theoretical skills and the practical ability to apply them to experiments. St Andrews presents an excellent opportunity for these interactions due to its world-leading experimentalists and the established collaboration that I have with them. The PDRAs will engage with both the local group and with my international collaborative network. They will learn to manage these interactions towards our scientific goals and important mentoring skills through their work with graduate students. My broader network of collaborations will provide good opportunities for progression of PDRAs. I am well-placed to guide them towards contacts in the financial and technology sectors should they ultimately choose to pursue careers beyond academia. b) PhD Students: The University of St Andrews is one of the host institutions for the Scottish Doctoral Training Centre (DTC) in Condensed Matter Physics. It is essential for the success of the DTC that it is embedded within world-class research groups. My team will form an important part of this environment and will help enhance the theoretical training of graduate students. Conversely, my research team will benefit from the elite graduate students that the DTC attracts and from its programme of international visitors. Materials and Technology: Although focused upon fundamental physics, the work proposed here is likely to have longer term, technological impact. Strongly correlated electron materials will play a key role in future technologies. The timing and extent of this impact is impossible to judge in advance of discovery, but it is essential for future industry. I have engaged with industry in a variety of contexts including GEC Marconi Research, Lucent Technologies Bell Labs (now Alcatel) and start up companies such as Cambridge Magnetic Refrigeration. I am well placed to seek appropriate channels of exploitation should occasion arise. Public Outreach: I am committed to public outreach. I have given presentations in Schools and Colleges, at the Royal Institution and various Cafes Scientifique, and run a Cafe Scientifique in St Andrews. These provide many opportunities to bring the results of my research to a broader public. This work plays an important role in inspiring young students into possible careers in science. They will mesh well with the outreach program of the DTC, which will be run by the PhD students, and the Gateway to Physics programme organised jointly between St Andrew and Heriot Watt. The latter aims to encourage students from less advantaged backgrounds into physics and engineering. Public outreach also fulfils an important cultural role. These are exciting times in theoretical physics with new links being forged between apparently disparate areas. I aim to share this with the public. I will encourage my PDRAs to become involved in outreach and have requested funds for them to attend media training courses.