Theoretical Physics – Quantum Condensed Matter. I am interested in systems of many quantum particles, where strong interactions lead to new states of matter. These new states can potentially be realized in experimental systems ranging from strongly correlated materials to dilute atomic gases confined to optical lattices. The intellectual challenge here is twofold. The first is to produce consistent theoretical models of such states, which already places strong constraints on the possibilities. The second is to interpret experimental data from these often complex systems to establish which of these novel states are actually realized in nature.
Fractionalization: Conventional theories of electronic matter assume that the electron is a well defined excitation, and are able to account for the properties of a number of materials. However, other materials like the high temperature cuprate superconductors where interactions between electrons are particularly important, show many phenomena that are strikingly unconventional. This led to the radical proposal that the electron breaks apart, or fractionalizes, in such systems, which could potentially explain many of these anomalies, although unambiguous experimental evidence for this is still lacking. Much theoretical progress has now been made in understanding electron fractionalization, in particular it is found to go hand in hand with an emergent gauge field. Remarkably, these ideas have also found applications in the area of quantum computing as well as a source of qubits that are naturally resistant to errors arising from decoherence. One of the attractive features of deconfined states is that they can naturally lead to dimensional reduction – excitations can be confined to planes or chains of a three dimensional systems - which could explain phenomena seen in different materials. I am interested in exploring further these exotic states of matter and their possible realizations in a variety of experimental systems.
Unconventional Quantum Phase Transitions: Recently, it has become clear that quantum phase transitions can also exhibit fractionalization, although the phases on either side of the transition are perfectly conventional. Remarkably, this allows for a (generically) continuous transition between states of very different symmetry, e.g. a superfluid, and a bond centered charge density wave. Such transitions are forbidden according to Landau’s theory of classical phase transitions, and appear here due to the presence of quantum interference effects. I will be pursuing this exciting new development, which may be the key to understanding certain puzzling quantum phase transitions seen in heavy fermion systems.
Phenomenology of Superconductor Quasiparticles: Finally, I am interested in the phenomenology of unconventional superconductors, such as the d-wave superconductivity observed in the cuprate materials. I have worked on developing a theory of heat transport in these systems in the vortex state that is in excellent agreement with experiments, and wish to extend this to studying other transport properties, such as the Nernst effect, just outside the superconducting state.