CAREER: Correlations, responses and dynamics of interacting topological matter

Princeton University, Princeton NJ

Investigators

Abstract

This award is funded in part under the American Rescue Plan Act of 2021 (Public Law 117-2). NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education to study novel phenomena and dynamical properties of topological states of strongly interacting electrons in materials. Topological states are a class of phases of matter which show properties that are robust against any local changes of the material, such as creating vacancies (missing atoms). An example is the topological insulator, which is insulating in the bulk, but has protected conducting electrons on its surface or edge. In contrast, a trivial insulator is insulating in both bulk and surface or edge. Certain topological states are particularly interesting as they host topological excited states which may be applied in quantum computation and information technologies. However, such topological states may only arise when electrons are strongly interacting and are difficult to realize. The PI aims at theoretically predicting and identifying such strongly interacting topological states in various materials. Promising systems include the so-called moiré materials which are engineered by stacking two-dimensional atomically thin materials at a relative twist angle, and two-dimensional metals in strong magnetic fields. The other focus of this research is to investigate the quantum dynamical evolutions of topological excited states in the interacting topological states, which are crucial for applications in quantum computation. Both analytical and numerical methods will be employed for these studies. The proposed research will advance our understanding and the technological applications of topological materials. This award will incorporate educational activities for undergraduate and graduate students. The PI will organize workshops and seminars with the support of the Princeton Center for Theoretical Science, providing the students opportunities to learn about topics at the forefront of condensed matter physics. The award will also contain outreach activities, including maintaining a group website to disseminate the team’s latest research to the non-scientific community, giving public lectures, and creating artworks bridging science and the broader interests of the general public. TECHNICAL SUMMARY This CAREER award supports theoretical research and education to investigate the correlated phenomena, topological responses and dynamics of interacting topological states, dominantly in low-dimensional quantum systems, and to explore their applications in quantum information. The PI will develop analytical models, perturbative and nonperturbative methods, and many-body numerical computations to perform the research. This research will focus on four directions: (1) Two-dimensional moiré systems from stacking and twisting of graphene and other layered materials. The PI will investigate the mechanism and topology of the correlated phases and superconductivity under Coulomb and electron-phonon interactions, and predict their experimental signatures. An important goal is to search for topological superconductors. (2) Competing phases in fractional quantum Hall systems. The PI will study the effective interactions between composite fermions or bosons from realistic Coulomb interactions between electrons, to investigate the origin of different fractional quantum Hall states observed in GaAs and graphene, and the competing ground states at half-odd integer Landau level fillings. (3) The mode reconstruction, quantum coherence, chaos and dynamics of generic interacting topological edge states and bulk anyons of two-dimensional topological matter, and the effects of interaction on the edge state interferometers. These studies will be further applied to propose quantum information devices. (4) The interaction effects and responses in three-dimensional topological phases of matter with defects and disorder, including the interaction induced three-dimensional quantum Hall effect, axion insulators and generic topological crystalline states. This award will incorporate educational activities for undergraduate and graduate students. The PI will organize workshops and seminars with the support of the Princeton Center for Theoretical Science, providing the students opportunities to learn about topics at the forefront of condensed matter physics. The award will also contain outreach activities, including maintaining a group website to disseminate the team’s latest research to the non-scientific community, giving public lectures, and creating artworks bridging science and the broader interests of the general public. 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.