Applications of Field Theory to Condensed Matter Physics

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education aimed at understanding condensed matter systems involving many strongly interacting electrons whose behavior is governed by strong effects of quantum mechanics. Advances in understanding could lead to the prediction of new states of matter with novel properties as well as new materials with potentially useful applications. A particular state of strongly interacting electrons is the “pair-density wave superconductor”, which is a quantum mechanical and superconducting analogue of molecules found in liquid crystal displays. It shares properties of both a solid and a liquid. The PI will further investigate whether such phases can explain the peculiar properties of materials known as high temperature superconductors. At sufficiently low temperatures, electrons in superconductors enter a cooperative quantum mechanical state that enables them to conduct electricity without any resistance. High temperature superconductors are interesting because they exhibit superconductivity at much higher temperatures than many other known classes of superconductors. The proposed pair-density wave state of matter may help explain how this is possible and how materials that exhibit superconductivity at room temperatures might be discovered. This could lead to virtually lossless transmission of electric power and other energy-related applications. The other focus of the research concerns understanding experiments seeking new states of matter. Of particular interest are those called topological states which are predicted to have unusual properties that would enable computation based on the laws of quantum mechanics. Such a computer could solve certain problems much faster than any currently existing computer. The research engages cutting edge problems in the physics of materials and provides opportunities to train the next generation of theoretical scientists at an exciting frontier. Research and education will be further integrated through the development of advanced curricular materials. Advances from the prediction and discovery of new states of electronic matter open new possibilities for future technologies related to advanced solid-state materials for electronic devices. TECHNICAL SUMMARY This project provides support for research into the theory of condensed matter and associated education. The objective is to understand condensed-matter systems involving many strongly coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics. The electrons in such strongly correlated systems organize spontaneously in electronic liquid crystal phases and topological phases. An unavoidable feature of these phases is that they naturally describe intertwined orders. They are closely related to mechanisms of high temperature superconductivity, a fundamental problem in physics which already has had a strong impact in technology. Topological phases are quantum fluid states of matter that do not have an order parameter, and therefore do not break any symmetry, but possess a kind of hidden quantum order in which the ground state degeneracy is determined by the topology of the space in which they exist. The quantum states of a topological fluid are strongly entangled, a property that can be used to devise a topological quantum computer, a frontier problem in physics and mathematics having great potential impact on technology. Related topics that will be investigated include the relation between electronic liquid crystal phases and high temperature superconductivity, quantum coherence and interference phenomena in quantum Hall systems, quantum entanglement and topological quantum computing. The PI will use the methods and ideas of quantum field theory, because they are natural approaches to attack problems involving the statistical and quantum physics of strongly interacting systems. Such an approach enables the project to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics. 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.