Novel Phases of Electronic Insulators and Quantum Hall Systems

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

Nontechnical Summary This award supports foundational theoretical research on the properties of a large collection of interacting electrons inside an insulating solid. The motion of these electrons is governed by the principles of quantum mechanics and is affected by the competition between the electron’s kinetic energy, and the inter-electron Coulomb repulsion. In the last few years, it has become possible to tune these different competing effects experimentally in several materials. Most striking amongst these are two-dimensional moire structures formed by bringing together two single-atom thick layers of materials whose lattices are slightly different. Fascinating phenomena have already been found in moire materials, and there is great promise for other profound future discoveries. This proposal will develop theoretical tools to study some of these phenomena and materials. The theory will be developed in the context of the many ongoing experiments on novel electronic insulators in moire, and other, materials. The goal is to provide a theoretical foundation and the tools needed to understand and predict the properties of these insulators. Fundamental research on electronic materials provides the foundational corpus upon which future electronic technological progress can build. Its focus on the quantum mechanics of systems with many degrees of freedom will potentially teach us many useful lessons as we seek to gain control over such systems and develop quantum technologies. The education component involves education at all levels, including undergraduate students at the frontiers of condensed matter theory. The Principal Investigator will convey the beauty of modern condensed matter physics to a broad audience outside this research field. Technical Summary This award supports theoretical and computational research, and associated education on the novel phenomena that happen in electronic insulators, and related quantum Hall systems. Specific areas of interest are the description of strongly correlated quantum particles that move in a topological band. This problem is central to certain moire graphene structures, and to quantum hall systems restricted to a single Landau level. The emphasis will be on general development of new theoretical concepts and field theoretic methods. When possible, these will be placed in the context of either experiments on specific materials or numerical work on specific microscopic models. Research will (1) address basic questions on strong correlation in a partially filled topological band inspired by ongoing experiments on quantum anomalous Hall states in moire graphene, and (2) continue the PI's development of a lowest Landau level theory to solve a wider range of problems, including fermionic quantum Hall states. A broad range of analytical and numerical methods will be employed. The overarching goal is to develop a theoretical framework to describe strongly interacting electrons in a partially filled topological band that can address both universal and non-universal aspects of the physics. Graduate and undergraduate students will be trained in modern condensed matter physics during this research. The PI will continue to design lectures to expose graduate students to experimental methods and the phenomenology of modern correlated materials. Lectures will be made widely available to the community. He will also continue his engagement with the high energy theoretical physics community to aid advances in both condensed matter and high energy 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.