This CAREER award supports theoretical research and education on the interplay between strongly correlated quantum materials and topological phases of matter. Strongly correlated quantum materials are solids in which the electrons behave collectively rather than an individual particles, while topological phases exhibit behavior that is insensitive to noise, defects, and impurities. Over the past decades, driven by these two topics, condensed-matter physics has witnessed great progress, with examples ranging from high-temperature superconductors to topological insulators and topological superconductors. These advances not only deepened our understanding of the quantum physics of many-body systems but also hold enormous potential for revolutionary applications, from commercial MRI machines and lossless power transmission to quantum computers that are no longer a futuristic concept. While historically the two areas of research have, in large part, developed separately, in recently years it has become increasingly clear that their synergy reveals even richer novel phenomena and greater potential for applications. One prominent example is the so-called moire flat-band materials, including the recently discovered magic-angle twisted bilayer graphene superconductor. When two layers of graphene are twisted relative to each other and the electron density varied, the system exhibits a variety of topological phases and unconventional superconducting phases. While potential applications abound, the fundamental mechanism for forming these phases is still under intensive investigation. These developments present an exciting opportunity for breakthroughs at the intersection of topology and correlation effects.

The PI will pursue the research goal in multiple directions. The PI will develop the ideas needed for a new topological quantum-computing platform based on the notion of higher-order topological phases, which seem featureless in the bulk and on the edge but host nontrivial states on the corners. The PI will uncover various kinds of topological superconducting phases in topological semimetals, which form an ideal playground for examining topology and interaction effects. To properly address the role of strong correlations, the PI will develop new theoretical and numerical approaches for quantum many-body systems that are not captured by perturbation theory and apply these approaches to topological systems, including morie flat bands. The closely related research topics addressed in this project will advance the forefronts of topological phases and their applications.

An integral component of this project is an education plan at high-school, undergraduate and graduate levels, with a specific emphasis on enhancing inclusion and diversity in academia and the STEM workforce. The PI will participate in existing programs at the University of Florida to reach out to high school students through lectures and direct mentorship on summer research projects. The PI will host a series of seminars in the physics department that focuses on career development within and outside academia. Via adapting and developing graduate-level courses, the PI will fill a gap in the training of junior condensed-matter physicists by bridging traditional topics and modern aspects such as topological phases.

By integrating outreach and education into the research plan, this work will provide young citizens of diverse backgrounds with unique learning and research experiences at the forefront of quantum physics and its potential applications, ensuring the success of the fundamental "Quantum Leap" identified by NSF as one of the "10 Big Ideas for Future Investment".

Technical Abstract

This project focuses on the intersection between topological phases of matter, in particular topological superconductivity, and strongly correlated systems. In the first part of the project, the PI will establish a new classifying framework for higher-order topological phases based on characterization of topological defects in topological insulators and topological ordered states. The PI will demonstrate the potential application of higher-order topological superconductivity as a new platform for braiding non-Abelian anyons. The second part focuses on demonstrating interacting topological semimetals as natural hosts of novel topological phases, including higher-order topological superconductivity and ultra-nodal topological superconductors with Bogoliubov Fermi surfaces. The final part is devoted to a close examination of theoretical models that admit topological superconducting instabilities. These models involve low-energy fermions in the vicinity of a quantum-critical point interacting with soft bosonic modes, which induce unconventional superconducting instabilities. To further understand the strong correlation and rich phases in these models, the PI will adopt and develop Quantum Monte Carlo methods and a Sachdev-Ye-Kitaev-like model that is exactly solvable in a large-N limit. In broader terms, these results will connect two thriving fields of condensed matter physics: unconventional superconductivity and topological phases of matter. Combining tools and ideas from both rapidly developing fields will tremendously deepen our understanding of quantum many-body physics.

The project also has three main educational components targeting students at different career stages. In collaboration with the University of Florida's Center for Precollegiate Education and Training, the PI will actively engage motivated high-school students through lectures on the basics of quantum computing and through individual research projects. With an emphasis on enhancing inclusion and diversity in academia and the STEM workforce, the education plan includes a series of seminars focused on career development for physics majors and physics graduate students. Through a long-term plan of special-topic and regular graduate courses, the PI will develop a new pedagogical framework for quantum many-body physics that naturally incorporates perturbative, non-perturbative, and topological aspects of these systems, which better suits modern research activities in condensed-matter physics.

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.

National Science Foundation (NSF)
Division of Materials Research (DMR)
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David Rabson
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University of Florida
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