This award supports theoretical research and education on unconventional superconductivity and exotic superconductors. This award has three related research thrusts. The first seeks to elucidate the role of broken symmetries that naturally appear in mesoscopic and nanoscale superconducting materials and at Josephson junctions. The second aims to determine the properties of superconductors near quantum critical points and to emphasize how these differ from conventional weak-coupling theories. The third will explore the origins of a sharp inconsistency between theory and experiment in the superconducting state of Sr2RuO4. The research will involve a combination of microscopic and phenomenological theories. This award also supports involving graduate and undergraduate students in the research. The PI aims to broaden participation of underrepresented groups through the inclusion of female graduate students and through the participation of undergraduates in the University of Wisconsin-Milwaukee Research Experiences for Undergraduates program. This program emphasizes the participation of minority and female undergraduate students. %%% This award supports theoretical research and education on unconventional superconductivity and exotic superconductors. Superconductivity has been discovered in single-wall carbon nanotubes and other nanostructures; mescoscopic superconductors have revealed new and intriguing behavior in magnetic fields. Superconductivity has been discovered in close proximity to a variety of magnetic phases in strongly correlated electron materials. The PI will follow thrusts in three important areas to elucidate the nature of superconducting states in nanoscale or nanostructured superconductors and exotic bulk superconductors. Exploring the role of quantum phase transitions, phase transitions that occur at zero-temperature, in determining the properties of the superconducting and normal states is a particularly timely aspect of this work. Quantum phase transitions appear to be important in understanding the exotic properties of superconducting states in strongly correlated materials, including the high temperature superconductors and some heavy fermion superconductors. The PI will also explore the origins of a sharp inconsistency between theory and experiment in the superconducting state of Sr2RuO4, likely an unconventional spin-triplet superconductor. The research will involve a combination of microscopic and phenomenological theories. This award also supports involving graduate and undergraduate students in the research. The PI aims to broaden participation of underrepresented groups through the inclusion of female graduate students and through the participation of undergraduates in the University of Wisconsin- Milwaukee Research Experiences for Undergraduates program. This program emphasizes the participation of minority and female undergraduate students. ***
