Novel phases of electronic insulators and quantum Hall systems

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on interesting new kinds of insulating phases of electronic solids. The electronic properties of most solids are understood within a quantum mechanical description that accounts for a large number of interacting electrons moving in the background of the charged atomic cores of the elements that comprise the solid. In simple solids the physics can be understood within an approximation that treats the electrons as quantum mechanical particles that move independently of one another. A major theme of modern materials research is on materials in which this approximation fails and the motion of different electrons is in fact correlated. Fascinating phenomena emerge in such materials; examples include high-temperature superconductivity, and other novel phenomena where the electrons appear to break apart inside the solid. An important recent experimental advance is the observation of such strong correlation of electronic motion in a particularly simple and tunable system, namely in atomically thin layers of graphene. The PI will develop new concepts and methods to deal with such electronic systems in diverse contexts. He will apply the lessons learnt from one platform, such as the graphene system mentioned before, to other known platforms that have long resisted understanding, and vice versa. Historically, such fundamental research on electronic materials has generated many of the concepts that underlie modern electronic technology. The proposed research will contribute to the continuum of scientific and technological knowledge that will enable future technology that harvests the quantum mechanical behaviors of systems with many degrees of freedom in fundamental ways. The research project will engage graduate students in cutting-edge research, and when appropriate and possible, undergraduates. TECHNICAL SUMMARY This award supports research and education on studying correlated electronic insulators in certain moire graphene structures, commonalities with quantum Hall systems, and of disordered frustrated quantum magnets. 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 of numerical work on specific microscopic models. The proposed projects in this broad area include: i) a study of microscopic models for the Moire superlattice in ABC-stacked trilayer graphene and related systems through a combination of analytical and numerical methods, ii) a microscopic Lowest Landau Level theory of a particular non-abelian quantum Hall state, seeking to establish analytically a theory that captures both topological and non-universal properties, iii) several general questions on disorder effects in 2D frustrated quantum magnets. The project will provide key insights and methods that will be useful in interpreting the results from experiments on Moire graphene systems, quantum magnets, and possible future cold-atom realizations of bosonic quantum Hall states. The PI will continue his efforts to design lectures to expose graduate students to experimental methods and the phenomenology of modern correlated materials. Undergraduates will be involved in the research when possible. He will also continue his engagement with the high-energy 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.