CAREER: Interacting Topological Bands in Moire Superlattices and Beyond

NONTECHNICAL SUMMARY

Quantum materials research is central to technological advancements. From the band theory of solids and its role in the semiconductor revolution to contemporary innovations such as quantum computers, advances in the theoretical understanding of quantum materials have been pivotal in shaping technological progress. Such an understanding hinges on establishing a connection between microscopic properties of materials and their emergent macroscopic behavior.

The PI aims to leverage recent advances in the realization of engineered moiré materials with tunable properties to explore such connection. The proposed research aims to establish links between the motion of a single electron on the microscopic scale, characterized by the topology and geometry of electron trajectories and their interaction with complex materials lattice patterns, and the macroscopic behavior of large swarms of interacting electrons in the same platform.

Since the properties of single electrons are simpler to study and easier to control, this provides a pathway to engineering the macroscopic properties of materials, potentially leading to the realization of novel phases of matter or those with enhanced properties for various applications.

The PI’s proposed education and outreach plan aims to address a significant knowledge gap in the public’s perception of quantum materials research. The goal is to inform and inspire high-school students to pursue careers in quantum materials research by engaging with Boston area high-schools. These efforts will target a broad audience including underrepresented minorities and students from economically disadvantaged backgrounds.

Additionally, the PI’s outreach efforts will disseminate knowledge about quantum materials research to a broader audience through the development of online materials that simplify advanced concepts and relate them to everyday experiences. Furthermore, the PI will develop a graduate course to help prepare the next generation of graduate students for research in the field of quantum materials research.

TECHNICAL SUMMARY

The research project centers on exploring the profound implications of band topology on strong interactions in complex material systems, with a particular emphasis on two-dimensional moiré platforms. The primary scientific problem addressed is the relationship between single-particle characteristics, such as quantum geometry of the electron wavefunctions and the configurational layout of moiré superlattices, and the emergent properties of the system under strong electron interactions.

The project is structured around three main objectives. First, the project will investigate the influence of quantum geometry on the formation and dynamics of exotic quasiparticles in interacting topological bands. These quasiparticles, such as skyrmions and anyons, arise from complex wavefunction structures unique to these systems, leading to new potential states of matter with applications in future technologies.

Second, the project will develop a framework for understanding topological band theory within quasicrystals, leveraging recent advances in creating moiré quasicrystals. This involves extending traditional topological concepts to quasicrystals, aiming to discover novel topological responses and strong correlation effects. Lastly, the project will seek innovative ways to realize time-reversal symmetric topological phases by exploiting intervalley coupling in moiré systems.

While most studies of fractional topological phases have focused on cases where time-reversal symmetry is broken, either explicitly or spontaneously, this research will explore conditions under which time-reversal symmetric fractional topological phases can be realized.

The PI’s proposed education and outreach plan aims to address a significant knowledge gap in the public’s perception of quantum materials research. The goal is to inform and inspire high-school students to pursue careers in quantum materials research by engaging with Boston area high-schools. These efforts will target a broad audience including underrepresented minorities and students from economically disadvantaged backgrounds.

Additionally, the PI’s outreach efforts will disseminate knowledge about quantum materials research to a broader audience through the development of online materials that simplify advanced concepts and relate them to everyday experiences. Furthermore, the PI will develop a graduate course to help prepare the next generation of graduate students for research in the field of quantum materials research.

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.