NSF-BSF: Theory of Quantum Materials

Stanford University, Stanford CA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research on atomic scale models of interacting electrons and ions in so-called "quantum materials". Some examples of quantum materials include high-temperature superconductors, two layers of carbon atom sheets on top of each other with a relative twist angle, and materials in which the electron-electron interaction energies are comparable or much larger compared to their kinetic energies. A major focus of this project is to unravel the mysterious properties of superconductors through which electrons flow in unison without losing any of their energy below a certain critical temperature. While quantum mechanics has allowed scientists to understand and predict most properties of "conventional" superconductors, achieving a fundamental understanding of unconventional superconductors, which include high-temperature superconductors and twisted layers of carbon atoms, has remained elusive. In this project, the PI and his team will study an array of atomic scale models on material systems and topics, including unconventional superconductors, that are at the heart of contemporary condensed matter physics. The quantum many-body problem that is the topic of this project has diverse and deep connections to other fields of physics, from string theory to quantum information. In addition, quantum materials have had a tremendous impact on both fundamental science and technology, and hence, an increased understanding of the problems to be investigated in this project has the potential to influence broader developments in science and technology. This award will also contribute to the development of the scientific workforce, as it will support the research training of graduate students and postdocs, who are likely to take leading positions in academia and industry in the future. TECHNICAL SUMMARY This award supports theoretical research on microscopic models of interacting electrons and phonons in quantum materials. Particular attention will be paid to the intermediate coupling regime, where interactions and kinetic terms are of comparable magnitude. Interactions are generally minimized when the constituent particles form suitable real-space structures, such as a Wigner crystal, while kinetic terms are diagonal in momentum space. Hence, the intermediate coupling regime is where quantum frustration is maximal. The PI will also apply a Landau-Ginzburg-Wilson effective field theoretical approach to study problems in which multiple distinct ordering tendencies are present, and the effective frustration reflects the competition between them. Specific problems of this general sort that will be the focus of study are (i) Solvable models of unconventional metallic regimes, particularly focusing on lessons for cuprate superconductors, (ii) Phenomenological and microscopic theories of systems with multiple intertwined ordering tendencies, including multiple possible uniform superconducting orders, pair-density-wave order, charge and spin density wave order, and electron nematic order, (iii) Correlated phases of multi-valley two-dimensional electron gases, and (iv) Generalizing the classification of distinct phases, especially unconventional superconducting phases, to quasi-periodic systems including Moiré materials in which Bloch's theorem does not apply and conventional symmetry classifications at the very least must be reconsidered. The quantum many-body problem that is the topic of this project has diverse and deep connections to other fields of physics, from string theory to quantum information. In addition, quantum materials have had a tremendous impact on both fundamental science and technology, and hence, an increased understanding of the problems to be investigated in this project has the potential to influence broader developments in science and technology. This award will also contribute to the development of the scientific workforce, as it will support the research training of graduate students and postdocs, who are likely to take leading positions in academia and industry in the future. 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.