Theories for Novel States of Matter Observed and Constructed in Condensed Matter and Cold Atom Systems

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NONTECHNICAL SUMMARYThis award supports research and education on developing theories for new states of matter that appear in materials and in systems comprised of arrangements of individual atoms at ultralow temperatures. The quantum mechanical behavior of interacting particles in these systems generates extremely rich physics and conceptual mysteries that continue to demand better and even revolutionary understanding from scientists. Recently, unexpected and exciting discoveries have been made in various condensed matter systems, such as devices made from two graphene sheets that can exhibit superconductivity when the two sheets are precisely stacked at a specific orientation with respect to one another. These systems offer unprecedented tunability and may represent the beginning of a new era of study in quantum many-body physics. Related recent progress in cold-atom experimental techniques allows the exploration of novel physics: under certain conditions, e.g. illumination by laser light of specific characteristics, these systems behave as if they exist in a higher-dimensional space than our usual three dimensions. This PI aims to develop and apply new theoretical concepts and methodologies to study the interplay of quantum mechanics and many-body physics in these platforms, and to develop theories for their manifestations in a variety of phenomena. The research could potentially lead to both new fundamental understanding of nature, and also to technological innovation from harnessing these strictly quantum phenomena. The project has potential scientific impact beyond condensed matter physics, as the research is relevant for high-energy physics. The PI expects to interact and collaborate broadly with scientists from related fields. The project will offer opportunities for training and mentoring graduate students and of postdoc researchers, providing them with essential theoretical tools that not only can be applied in physics research within academia but can also find uses in a wide range of industrial settings.TECHNICAL SUMMARYThis award supports research and education on unconventional states of matter in condensed-matter and cold-atom systems. The goal of this project is three-fold: i) to describe and understand the recently discovered superconductivity and the weakly correlated insulator phase in moire superlattices via a formalism developed by the PI's group recently, and to also engineer more exotic states of matter in related systems; ii) to construct and understand unconventional states of matter such as strongly interacting topological states and symmetry-protected topological states in high dimensions that can be realized in cold atom systems with synthetic dimensions; iii) to use the exactly soluble Sachdev-Ye-Kitaev physics as the starting point to describe and understand non-Fermi-liquid states and related phenomena that are experimentally observed in high-temperature superconductors.The project has potential scientific impact beyond condensed matter physics, as the research is relevant for high-energy physics. The PI expects to interact and collaborate broadly with scientists from related fields. The project will offer opportunities for training and mentoring graduate students and of postdoc researchers, providing them with essential theoretical tools that not only can be applied in physics research within academia but can also find uses in a wide range of industrial settings.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.