Interactions and symmetry breaking in Dirac systems

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Graphene, one-atom-thick layer of the more familiar graphite, has been fabricated in 2004, and has brought the Nobel prize last year to its inventors. It is an extremely strong, yet deformable, well-conducting membrane of carbon atoms. Its discovery promises to revolutionize electronics, and has already forced physicists to revise and reexamine many of their cherished theories of how solids conduct electricity. I propose to theoretically study how the Coulomb interaction between electrons affects the conducting properties of graphene and other closely related new materials. It turns out that this seemingly straightforward question in fact hides a difficult and general physical problem. There is already a number of poorly understood anomalies that occur in graphene, observed in magnetic field or under mechanical strain. In the last six years my group at Simon Fraser University has been developing a general mathematical formalism that should describe the effects of the repulsion between electrons. One part of the proposal is to use our calculational tools to devise and understand the ways of controlling conducting properties of graphene, by mechanical deformations, among other methods. This should make graphene closer in its conducting properties to silicon, the current alpha and omega of commercial electronics. The other part is to explore the unique electronic structure of graphene to study novel physical phenomena that occur when graphene is turned into an insulator, or even into a superconductor. The hope here is that the new physics one may learn this way may apply to the whole class of new materials that share certain aspects of graphene, and may even help our understanding of some fundamental issues in high-energy physics, such as how elementary particles acquire their mass.