Strongly correlated quantum materials

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Much of today's industry relies on advanced materials whose development from discovery to commercial product takes decades. Even private foundations in the United States, such as the Moore foundation and the Simons foundation, recognize and support fundamental research that will provide a wealth of practical information that entrepreneurs and innovators will be able to use to develop new products and processes. This type of fundamental research is as important for Canada as it is for the United States and the world. The students that will participate in the development of fundamental knowledge will be especially skilled to recognize the opportunities brought about by this knowledge and to understand the advantages and limitations of the tools necessary to apply fundamental research. We will contribute to this effort by focusing on "Strongly Correlated Quantum Materials", namely materials with pronounced quantum behavior and collective effects that lead to a host of properties that are intriguing from a fundamental point of view, while also technologically relevant. This five-year research program has two broad classes of objectives. The first direction uses the most powerful methods currently available, some of which my group has developed, to predict properties of strongly interacting quantum materials. Specific examples include strongly-correlated superconductivity. Superconductors transport electricity without resistance and manifest quantum effects at macroscopic scales. Superconductivity at room temperature would revolutionize technology. Strongly-correlated superconductivity pushes theoretical methods in the most difficult regime, namely in the vicinity of a metal-insulator transition, where the localized and wave picture of electrons are equally important. Superconductivity is strongest near this metal-insulator transition, whether it is induced by adding/removing conduction electrons, as in ceramics based on copper-oxygen planes (cuprates), or by pressure, as in layered organic compounds. By keeping this general point of view, where cuprates and layered organics are considered within the same framework, we can firmly establish which methods give us a predictive theory of strongly correlated superconductivity. The second direction develops new methods, taking advantage of quantum simulators such as cold atoms for benchmarks, and taking advantage of insights from other fields, such as quantum information, to predict and propose measurements of new quantities. Indeed, although traditional theoretical methods using the most elementary notions of quantum mechanics were sufficient to obtain the basic knowledge that gave us the materials that make up current electronic technology, they are inadequate for strongly correlated quantum materials. We are addressing a grand challenge of modern physics: developing the tools necessary to handle subtle quantum mechanical aspects of materials to make useful predictions.