Current Research
Exciting new electronic materials studied extensively over the last decade
range from organic and cuprate superconductors to semiconductor quantum wires.
The explanation of fascinating properties such as high-temperature
superconductivity and unconventional metallic behaviour represent a considerable
theoretical challenge. This is because many of the theoretical methods used
successfully to describe the weakly interacting electrons in conventional metals
and semiconductors (e.g., copper and silicon) are not applicable to these
systems in which the electrons interact strongly with one another and are
confined to move in zero, one or two dimensions.
(For further background information)
Models of
strongly interacting electrons in low dimensions
These materials have many properties similar to high-temperature superconductors, including competition between insulating, quantum antiferromagnetic, superconducting, and exotic metallic phases. Given a model Hamiltonian which includes the interactions between the electrons the challenge is to calculate the properties of its ground state and excited states and compare to the rich phase diagrams observed experimentally.
Most phase transitions in nature are driven by thermal fluctuations; examples include ice melting or heating a ferromagnet into a paramagnet. Quantum phase transitions occur at zero temperature and are driven by quantum fluctuations. They are important to understanding properties of many strongly correlated electronic materials. Such transitions can persist in the presence of disorder due to impurities but they exhibit an even richer physics. For example, ensemble averages are dominated by rare configurations. Due to the theoretical complexity of this problem the focus in on studying the simplest possible model Hamiltonians which exhibit the relevant physics and not making approximations.
Future computer technology will make use of ultrasmall electronic devices such as quantum dots and single electron transistors whose properties are dominated by quantum effects. In the presence of disorder large statistical fluctuations in the electrical resistance are observed. The associated theory has a rich mathematical structure and is being investigated with members of the UQ Centre for Mathematical Physics.
Recent experiments have shown that electrons can travel large distances along the double helix of DNA without losing the coherence of their wavefunction. Model Hamiltonians for this process, which take into account the base pair sequence and the interaction with the environment are being investigated.