CAREER: Frontiers of Superconductivity: Unconventional, Topological, and Low-Density Systems

About This Grant

NONTECHNICAL SUMMARY Superconductivity — the ability of certain materials to conduct electricity with zero resistance — was one of the landmark discoveries of twentieth-century physics. It revolutionized technology, enabling powerful magnets for particle accelerators and MRI machines, maglev trains, and today serves as a promising foundation for quantum computing. Superconductivity also deepened our understanding of nature by revealing a remarkable quantum state visible on macroscopic scales. Yet, even after decades of research, many superconductors defy conventional explanations. They appear and persist under conditions where standard theory predicts they should not exist, leaving the mechanisms behind them largely unknown. This project seeks to uncover how superconductivity emerges in these unconventional systems — specifically those with very low electron density and strong electron-electron repulsion, both normally hostile to superconductivity. By studying representative materials where unusual behavior is observed, the PI will identify plausible microscopic mechanisms, evaluate them against experimental data, and propose new measurements to distinguish between competing scenarios. This effort will clarify how exotic superconducting states form, what makes them unique, and how they might be engineered or controlled. Ultimately, the results will guide the search for new superconducting phases and advance their potential use in future technologies. The educational component aims to broaden participation in science and strengthen the future quantum workforce. The PI will expand undergraduate involvement in theoretical physics research and spark scientific interest among high-school students and educators in the Pittsburgh region. Outreach activities — conducted through the Sigma Xi honorary research society and in collaboration with Carnegie Mellon’s Eberly Center and Leonard Gelfand Center — will include public lectures, science fairs, teacher-facing workshops, and hands-on research engagement events. A key objective is to lower the barriers that students often face when entering theoretical physics. To this end, the PI will promote research opportunities and organize networking events for Carnegie Mellon undergraduates, helping them build the skills and connections needed to pursue careers in physics and quantum science. TECHNICAL SUMMARY Many experimentally confirmed superconductors fall outside the scope of conventional Bardeen-Cooper-Schrieffer theory. Particularly intriguing are systems with low carrier density, strong Coulomb repulsion, and non-trivial band topology, where superconductivity emerges despite conditions that should strongly disfavor pairing. The main challenge is to identify the microscopic mechanisms responsible for pairing in these regimes. Although numerous theoretical proposals exist, they often lack definitive, experimentally distinguishable predictions. This project will address this gap by developing and analyzing candidate pairing mechanisms in low-density and strongly interacting superconductors, and by formulating measurable signatures that discriminate among competing theories. The research will explore how strong electron-electron interactions promote or suppress superconductivity, determine the regimes in which pairing survives at vanishing carrier density, and establish routes toward realizing topological superconducting states. To differentiate pairing scenarios, the PI will compute experimentally accessible observables — including penetration depth, specific heat, upper critical field, and collective modes — as functions of temperature, magnetic field, and carrier density. These results will enable ruling out incompatible mechanisms and identifying those consistent with experimental trends. By comparing theoretical predictions with existing data and proposing new targeted probes, the project aims to reveal the microscopic origin of pairing in representative materials. The outcomes will advance the understanding of unconventional superconductivity, guide the discovery of new superconducting phases, and clarify connections to other correlated systems, possibly including high-temperature superconductors. The educational component aims to broaden participation in science and strengthen the future quantum workforce. The PI will expand undergraduate involvement in theoretical physics research and spark scientific interest among high-school students and educators in the Pittsburgh region. Outreach activities — conducted through the Sigma Xi honorary research society and in collaboration with Carnegie Mellon’s Eberly Center and Leonard Gelfand Center — will include public lectures, science fairs, teacher-facing workshops, and hands-on research engagement events. A key objective is to lower the barriers that students often face when entering theoretical physics. To this end, the PI will promote research opportunities and organize networking events for Carnegie Mellon undergraduates, helping them build the skills and connections needed to pursue careers in physics and quantum science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.