Interaction Effects and Topology in Relativistic Quantum Materials

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Quantum mechanics and Einstein's theory of relativity form two fundamental pillars of modern physics. Traditional condensed matter physics depends heavily on the first one of these — most material properties are inherently quantum mechanical -- with relativity playing only a minor role. Beginning in 2005 condensed matter physics underwent a profound and rather unexpected revolution, which in the hindsight could be termed “relativistic”. It culminated in the discovery of a new form of matter called topological insulator (TI). In these novel materials quantum mechanics and relativity combine to produce a remarkable outcome: TIs can be described as crystalline solids whose bulk is insulating (does not conduct electricity) but whose surfaces are metallic and thus good conductors. In the past decade topological insulators have been extensively studied and numerous solids have been experimentally identified as TIs. Rich experimental programs to test for the variety of theoretically proposed phenomena associated with them are now ongoing. Worldwide effort to harness their unique properties for practical applications is also underway. A parallel study of the related class of materials called topological superconductors (TSCs) has also been initiated. Thus far we do not have a confirmed experimental realization of a natural TSC material but certain artificially engineered structures are thought to behave as TSCs. This proposal is concerned with theoretical explorations of novel quantum phenomena in topological insulators and superconductors.******The main goal of the proposed research is to develop understanding of the effect of interactions between electrons in these novel states of relativistic quantum matter. The intersection of topology, relativity and interaction physics is a new and largely uncharted frontier of condensed matter research. The band theory of solids that forms the foundation of our understanding of these materials assumes that interactions are weak and can thus be neglected. While this is a valid assumption in many crystalline solids there are also important instances when the assumption fails. Strong interactions then give rise to new states of matter, fundamentally impossible in non-interacting systems. Well known examples of such interaction-enabled phases of matter include Mott insulators, high-temperature cuprate superconductors, certain quantum magnets and the fractional quantum Hall liquids. Historically, discovery of each of these material classes opened up new areas of inquiry, established new paradigms and enabled key advances in devices and technologies. The proposed research will seek to establish new paradigms for interacting topological quantum matter, paradigms that are experimentally testable and likely to inform future technologies.**