Condensed matter systems provide a natural laboratory for studying novel phenomena in quantum many-body physics. Superconductivity, superfluidity and magnetism are examples of spontaneous symmetry-breaking driven by quantum effects. My research is directed at understanding these phases of matter whose existence depends on the interplay of quantum interference, strong interactions and disorder. The techniques I use include a combination of analytical and computational methods.
For reviews on some of the following topics, see:
D.K.K. Lee and A.J. Schofield,
Correlated Quantum Fluids and the Search for a New Theory of Metals [ PDF (300Kb), postscript (900Kb) ]
Metals Without Electrons [ PDF (570Kb) ]
The first article contains a few more technical details than the second.
A two-dimensional electron gas exhibits the quantum Hall effect in a strong magnetic field. Its Hall resistivity is quantized in units of h/e2. This reflects the presence of distinct Landau levels in the energy spectrum. The high degeneracy of the states within each Landau level means that the system is highly sensitive to interaction and disorder effects, giving rise to a variety of exotic ground states. [more]
The cuprate superconductors are unconventional not only because of the relatively high temperature at which they become superconducting - they are far from an ordinary metal even in the normal state above the superconducting transition temperature. An understanding of this "strange metal" requires a radical revision of the conventional Fermi liquid theory of electrons in solids. [more]
Impurities are unavoidable in many condensed matter systems. Although they may be a nuisance in many cases, disorder effects offer an interesting opportunity to study the physics of quantum interference. Whereas classical particles move diffusively when randomly scattered, quantum particles/waves may become totally localized. This Anderson localization is exhibited by electrons in dirty metals and photons in disordered dielectrics. [more]
Liquid 4He is a Bose fluid which becomes superfluid
below 2K. It exhibits zero viscosity and vortices have
quantized circulation. Experiments on helium in porous media show that
this is a delicate state of matter easily destroyed by disorder. This
superfluid-insulator transition is also found in
superconducting thin films where the bosons are Cooper pairs.
The nature of the insulating state, the "Bose glass", remains a puzzle.