Théorie et simulations par ordinateur des matériaux quantiques et de la supraconductivité/ Theory and computer simulations of quantum materials and superconductivity

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Much of modern technology owes to our deep understanding of electronic properties of materials. That understanding is rooted in intertwined empirical, experimental and theoretical knowledge. I work on the theoretical aspects of electronic properties of materials, in other word I design and solve mathematical models and perform large scale computer simulations to understand new materials that escape conventional understanding. In materials such as high temperature superconductors, contrary to the usual case, the electrons interact so strongly with each other that they would in fact prefer not to carry electricity; they should be in an insulating state. It is by changing slightly the number of electrons by chemical means that one is lead to a new type of superconductivity that occurs at much higher temperature than usual. In the last few years several breakthroughs have occurred, in terms of new materials, new theoretical understanding and new spectacular experiments. We contributed to some of the theoretical breakthroughs. We believe that we are in a position to answer questions such as: What are the appropriate mathematical tools to predict the behavior of electronic systems that show both localized (magnetic) and propagating (superconducting) character? Can we use these tools to show that there are new elementary excitations, or concepts (pseudogap) that could summarize and explain in a simple way the anomalous properties of these systems (i.e. find concepts that will do what the concept of "holes" did for the semiconductor industry)? Can we also use these concepts in related classes of materials? What is the origin of high temperature superconductivity? Answering such questions should help people in my field to develop materials that may have other striking and technologically useful magnetic or electrical properties and also exhibit new phases of matter. Answering such questions will also help in the quest for materials that could exhibit superconductivity at room temperature. Since superconductivity manifests quantum properties on a macroscopic scale, one can foresee in the long run the birth of revolutionary technologies, such as the quantum computer, and corresponding new industries.