A single mathematical idea—the Higgs mechanism—explains both why magnets levitate above superconductors and why particles have mass, and this research aims to find more such unifying principles at the boundary where quantum rules give way to everyday classical behaviour. Condensed matter physics already underpins transistors, hard drive read heads, and superconductors, but many materials display "quantum critical" behaviour that obeys a hybrid of classical and quantum rules. Current theory cannot fully explain how the familiar classical world emerges from the microscopic quantum one, and experimental anomalies in these materials point to missing fundamental principles. This is a theory-driven project that develops mathematical models predicting new quantum effects, then works with experimentalists to test them. If successful, it could reveal general laws governing how quantum behaviour scales up—laws that may eventually guide the design of quantum computers or novel electronic materials. The work is primarily curiosity-driven fundamental science, but the same symbiosis between theory and experiment that produced the Higgs mechanism in particle physics began with a puzzle about levitating magnets. Deeper understanding of quantum critical systems could similarly open unexpected technological routes.
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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.
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