Grant: Discovery Grants Program - Individual

At the atomic and sub-atomic level, the physical behaviour of matter must be described by quantum mechanics. This is a fascinating and mysterious realm where the determinism of classical physics fails and an object can be in two different states at the same time - a famous (but unrealistic) example being Schroedinger's cat, which could be simultaneously alive and dead. Quantum mechanics plays an important role in the behaviour of solids and fluids in some parameter regimes and its understanding played a crucial role in the semi-conductor revolution, responsible for much of modern technology. The understanding of the quantum mechanical behaviour of a macroscopic number of interacting particles, such as electrons in a solid or helium atoms in a liquid, is an extremely challenging field. in some cases, the interactions between the particles are adequately treated using simple models but there are other situations where the simple models fail dramatically and new understanding is called for. These go under the name of strongly correlated systems. Theoretical and experimental progress in this field is expected to play an important role in future technologies such as quantum computing and spintronics.* I propose to do theoretical research in several areas of strongly correlated systems which are also fields of considerable current experimental activity. These include:*1) Topological materials: Revolutionary discoveries of the past decade have shown that some materials while having rather conventional bulk behaviour can exhibit novel quantum mechanical behaviour on their surfaces or edges, of potential importance for applications. I plan to explore the interactions between these novel edge excitations and ordinary electrons.*2) Graphene: This material consists of a single layer of carbon atoms, first fabricated and studied in 2004. It exhibits many fascinating properties and offers various possibilities for new technologies. It has been claimed theoretically that the edges of graphene ribbons may exhibit ferromagnetism, even though the bulk of the ribbon is non-magnetic. This phenomena has not yet been observed experimentally although rapid developments in experimental techniques may make it possible soon. I plan to extend my previous rigorous results on the existence of this magnetism in a simplified model to more realistic models.*3) Superfluid helium in nano-pores: Helium is the unique element which remains in a liquid phase down to a temperature of absolute zero and exhibits superfluid behaviour at low temperatures, corresponding to frictionless flow through narrow pores. However, when these pores get narrow enough, in the nano-metre range, the behavior starts to change due to strong correlation effects which I plan to continue studying. *