Correlated Quantum Systems: Topological Phases, Non-Fermi-liquids and Entanglement

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The aim of my research program is to understand the different ways that electrons can organize themselves in solids. Amazingly, the basic laws of quantum mechanics, together with simple electrostatic interactions governing electron motion, give rise to a great array of different phases of matter, such as metals, insulators, superconductors, and magnets. In the last ten years, an entirely new class of phases of matter was discovered: topological insulators. The bulk of these materials does not conduct electricity, however the surface does. One may think that this is an accident and that one can cut the conducting surface layer away, but in fact, any cleave of the bulk material always exposes a new conducting surface. A primary goal of my research program is to classify all such bulk topological insulators and related phases of matter and to understand their surface behaviour. This direction of research addresses fundamental questions at the forefront of solid state physics, provides a link to active areas in modern mathematics, such as topology and category theory, and furthermore, paves the way for technological applications of topological phases of matter in quantum computing. Aside from studying exotic insulators, I am also pursuing unusual conductors (metals). Simple metals, like copper, are very successfully described by Landau Fermi-liquid theory, however, there are a number of materials, collectively referred to as “strange metals,” whose behaviour strongly deviates from Fermi-liquid theory. These include cuprate, iron-arsenic and certain heavy-fermion material families. Like simple metals, strange metals often turn superconducting when the temperature is lowered below a critical temperature Tc; however, the magnitude of Tc is often much higher than in simple metals. A goal of my research program is to develop a theory of strange metals and their superconducting instabilities - a necessary first step in the long-term effort to systematically design new materials with high superconducting Tc for application purposes.