Correlation Effects in Topological Insulators

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The laws governing the behavior of individual electrons and atoms are simple, elegant, and few. But then how can we account for the endless variety of forms which we observe matter to assume? Condensed matter physics seeks to explain these observations and to discover new states of matter. Distinct states of matter can be thought of as distinct patterns into which a group of electrons or atoms can organize themselves, just as a group of dancers can perform different choreographies. A fascinating question in this field is how many such patterns are consistent with the laws of quantum mechanics, and lead to quantum states of matter.The recent discovery of topological insulators (TIs), a new quantum state of matter, triggered a veritable explosion in condensed matter physics. As their name suggests, TIs are topologically distinct from conventional insulators. Topology, the mathematics of the global properties of geometrical shapes, states that two geometrical shapes are topologically distinct if they cannot be smoothly deformed into one another. All insulators can be described mathematically by abstract geometrical shapes. The abstract geometrical shape describing a conventional insulator cannot be smoothly deformed into one describing a TI, in the same way that a rubber band cannot be transformed into a Möbius strip without first cutting it. This mathematical distinction reveals itself in the physical properties of TIs. TIs, like ordinary electrical insulators such as diamond or silicon, do not allow electrical currents to flow in their interior. Unlike ordinary electrical insulators, TIs do conduct electricity on their surface, and do so almost without dissipation. If this striking physical property can be harnessed in microprocessors, TIs could enable the design of smaller and more efficient mobile computing devices. The surfaces of TIs might also provide the essential ingredient for a quantum computer, a computational device based on the laws of quantum mechanics that is poised to operate exponentially faster than a conventional computer.The first few years of theoretical TI research, including my own work, focused on idealized models of TIs that ignored the electrostatic repulsive force between electrons. Recent experimental and theoretical developments, as well as the goal of designing viable microelectronics applications, are now pointing the field in a new direction. There are indications that interactions between electrons may lead to novel and unexpected phenomena and even enhance the potential of TIs for applications. By focusing our research on largely unexplored regimes where electrons inside a TI interact strongly with one another, we will contribute to our basic understanding of quantum states of matter and hope to further their use in real-world applications. Our investigations into key issues in the field of TIs will help maintain Canada’s leadership in quantum materials research.Combined with other sources of funding, this NSERC Discovery Grant would support the training of eight personnel – undergraduate and graduate students, and postdoctoral fellows – to high levels of expertise in the tools of the trade of modern condensed matter theory. This includes a variety of advanced analytical and numerical skills that are broadly applicable inside and outside of academia, and will contribute to growing Canada’s knowledge-based economy.