Topology, interactions, and disorder in exotic quantum materials

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Ordinary phases of matter-solid, liquid, and gas-are distinguished by emergent macroscopic properties, such as rigidity or the lack thereof, which are a consequence of how atoms microscopically arrange themselves, but also transcend the minute details of such arrangements. At temperatures near absolute zero, quantum effects allow for qualitatively new patterns of microscopic arrangements that produce novel emergent properties beyond those of ordinary matter, such as superfluidity, magnetism, and superconductivity. The field of quantum materials, a key subdiscipline of condensed matter physics, attempts to theoretically understand such quantum phases of matter and the transitions between them, and to experimentally discover materials that realize them. In the past ten years or so, this field has witnessed a veritable revolution. Recognized in part by the 2016 Nobel Prize in Physics, the prediction of topological insulators-where an insulating bulk coexists with a robust metallic surface-has received wide experimental confirmation and evolved into a thriving branch of mainstream condensed matter physics. The discovery of exotic magnetic materials where quantum "fuzziness" is so strong as to completely demagnetize them may signal the long-awaited discovery of the spin liquid, an exotic quantum state of matter first theorized in the 1970s. The unusual behavior of ultrathin materials in strong magnetic fields reveals new cooperative behaviors previously thought impossible, such as the emergence of collective excitations with only a fraction of the charge of an electron. Many of the unusual properties of those exotic quantum materials, such as metallic surface states and fractionalized excitations, may lead to novel technological applications in low-power electronics and quantum computing. A necessary first step towards such applications, the development of a complete theoretical understanding of this bewildering variety of new phenomena is however hindered by the lack of a unified conceptual framework and complicated by the unavoidable presence of imperfections and impurities in real materials. Supported in part by this NSERC Discovery Grant, my research program aims to achieve a deeper and more unified understanding of three broad classes of quantum materials-topological materials, spin liquids, and ultrathin materials in high magnetic fields-through the construction of mathematical models that incorporate both quantum effects and material imperfections, and the analysis of those models via cutting-edge theoretical methods. By training undergraduate research assistants (URAs), graduate students, and postdoctoral fellows (PDFs) in a wide range of broadly applicable analytical and computational skills, this research will help maintain Canada's leadership in the field of quantum materials and will contribute to grow our country's knowledge-based economy.