Strong Electron Correlations and Quantum Critical Phenomena

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This award supports theoretical research and education in condensed matter physics with a focus on aspects of strongly correlated electron phenomena. Three key ideas lie at the heart of this project: 1) spectral weight transfer across the Mott gap suggests that the correct low-energy theory of doped Mott insulators involves a charge 2e bosonic field, 2) the suppression of the Josephson effect in nanowires below a critical diameter originates from the onset of a superconducting state with a pairing symmetry that is orthogonal to the s-wave state in the leads, and 3) the origin of the metallic state in thin metal film alloys displaying a putative insulator-superconductor transition is driven by glassiness. The goal of this project is to confirm and elucidate each of these ideas. This project focuses on developing theoretical tools and new ideas to elucidate key experimental systems that are dominated by large Coulomb repulsions or systems near quantum critical points. Of course in the presence of disorder, new phases are possible, such as glasses. Precisely how metallic phases obtain in two dimensions for either bosons or fermions is not known. This project continues to develop a possible resolution of this problem, as well as a systematic way of approaching many aspects of the strongly correlated problem. Broader Impact: This award supports graduate students seeking their PhD degrees in theoretical solid state physics. As the large Coulomb repulsion and disorder problems are central to solid state physics, it is essential that students gain expertise in this area. In addition to the training of graduate students, several other broad educational goals will be met. First, as a result of the PI's commitment to the communication of the current status of theoretical solid state physics to the next generation of students, he has written a much-needed graduate textbook, "Advanced Solid State Physics." The PI plans a new edition will which will incorporate new material on strongly correlated systems which helps integrate forefront research into an educational text. A new course at Illinois, entitled "Quantum Phase Transitions," has been developed as a direct outgrowth from NSF-funded research. A second important feature of this project is the PI's impact as a highly visible and effective role model for minority students in the Department of Physics and the College of Engineering (COE) at Illinois. A novel outreach component of the project is the PI's involvement in assisting scientists in developing countries. He recently organized an international workshop in Trinidad and Tobago on "Mottness and Quantum Criticality" which helped to introduce scientists from the Caribbean to frontier problems in strongly correlated electron materials. In addition, the PI is the Chair of the organizing committee for the symposium and educational and museum outreach for the 50th anniversary of the publication of the Bardeen-Cooper-Schrieffer theory of superconductivity. NON-TECHNICAL SUMMARY:This award supports theoretical research and education in condensed matter physics. The proposal focuses on the discovery and understanding of new states of matter that occur when the interactions among electrons are very large and lead to strong correlations in their motion. High temperature superconductors are examples of a class of materials in which strong interactions among electrons lead to new states of matter. Among the states of matter that the PI will study are the insulating state that arises as a consequence of strong interactions among electrons, known as a Mott insulator, and new states of matter that may be hidden in a transformation that takes place between superconducting and insulating states observed in thin films. The PI will focus on developing theoretical tools and new ideas to elucidate the underlying physics of key experimental systems and to understand how new metallic states arise.The PI is a highly visible and effective role model for minority students in the Department of Physics and the College of Engineering (COE) at Illinois. This award supports some of his education and outreach activities, including graduate level education in theoretical condensed matter physics with a focus on central problems of the field. The PI's research will contribute to his work to create a new edition of his graduate level textbook, "Advanced Solid State Physics," which will incorporate new material and integrate forefront research into the text. The PI activities in assisting scientists in developing countries to modernize their research constitute an outreach component of this project. His activities as Chair of the organizing committee for the symposium and educational and museum outreach for the 50th anniversary of the publication of the Bardeen-Cooper-Schrieffer theory of superconductivity are another component of his outreach efforts.