CAREER: Monopole Superconductivity and Ferromagnetism of Itinerant Electrons

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NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education in unusual states and fundamental questions that arise in the study of metallic materials. A piece of metal contains many electrons that are moving and interacting with each other. Quantum mechanics governs their collective behavior, which can give rise to new states of matter manifesting as electron order. Consider an example of order from our everyday classical world, a team of swimmers can control and change their position as a whole by performing a synchronized change in the shapes their bodies assume. An analogous phenomenon in quantum systems is called many-body Berry phases: due to quantum mechanical effects, electrons in a material can synchronize and exhibit collective effects. The electrons can be induced to organize in many different ordered states, some of which have not been observed before. This project advances fundamental concepts by exploring the mathematical description of order as well as its physical consequences. The project can potentially lead to developing a new platform for quantum computation.The PI will also tackle the long-standing problem of uncovering the microscopic mechanism behind the magnetism some metals exhibit. This is a formidable problem because of the failure of a common theoretical assumption, namely that electrons moving in a crystal of atoms can be considered independently. In fact, the motion of any one electron is strongly correlated with the motion of all others. The PI and her research team will combine analytic and numerical methods to tackle this challenge. Apart from theoretical insight, the project could lead to technological applications that harness these strong correlation phenomena.This award will enable a range of educational and outreach activities, from mentoring graduate, undergraduate, and high-school students, to developing new course materials aligned with the research project that cover the application of modern mathematical approaches in condensed matter physics. The PI will also initiate an interactive community outreach program targeting Pre-K and K-12 students and their parents, aimed at enhancing the public's interest in and appreciation of quantum physics and the research frontier.TECHNICAL SUMMARYThis CAREER award supports theoretical research and education in new quantum phenomena of itinerant electrons arising from the interplay of topology, interaction, and strong correlation. Specifically, the PI will focus on developing a theory framework for new classes of many-body topological states, and on a nonperturbative approach to itinerant ferromagnetism in strongly correlated multiorbital systems. The PI and her group will investigate novel classes of three-dimensional topological many-body ordering states characterized by monopole harmonic symmetries, including both superconducting and density-wave states. The particle-particle (Cooper) pairing, or, particle-hole pairing, inherits nontrivial Berry phases from Fermi surface topology. Their gap functions cannot be globally well-defined in momentum space, and thus go beyond the standard realization of rotational symmetry based on spherical harmonics. Consequently, they exhibit topologically protected nodal structures regardless of specific ordering mechanism and can only be characterized by monopole harmonic functions.Itinerant ferromagnetism is the ferromagnetism of mobile electrons based on Fermi surface instabilities rather than the ordering of local spin moments. However, it lacks a well-controlled weak-coupling description; a precise answer to the relation between orbital degeneracy and the mechanism of ferromagnetism has so far been lacking, mostly due to the lack of nonperturbative results for handling strong magnetic fluctuations. The PI and her group will develop nonperturbative methods, combining analytic approaches and unbiased numerical simulations, to study the role of orbital degeneracy in the mechanism of itinerant ferromagnetism and strong correlation effects of itinerant electrons close to ferromagnetic transitions.This award will enable a range of educational and outreach activities, from mentoring graduate, undergraduate, and high-school students, to developing new course materials aligned with the research project that cover the application of modern mathematical approaches in condensed matter physics. The PI will also initiate an interactive community outreach program targeting Pre-K and K-12 students and their parents, aimed at enhancing the public's interest in and appreciation of quantum physics and the research frontier.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.