Topological Order and Symmetry Breaking in Condensed Matter Physics
The main directions of Professor Fradkin’s research are the theory of topological phases in condensed matter and the theory of electronic liquid crystal phases. One exciting feature of his research is that it combines fundamental problems in quantum mechanics and quantum field theory with experiments at the leading edge of technology. The recent discovery of materials known as topological insulators, for example, has opened the possibility of creating a topological quantum computer by combining topological materials with superconductors and high-temperature superconductors.
Over the past decade Professor Fradkin has been working on the theory of high-temperature superconductors within the conceptual framework of electronic liquid crystal phases–that is, phases whose microscopic constituents are electrons that carry both charge and spin. He and his colleagues have concluded that these phases must also include novel phases in which the superconducting state itself might also behave as a nematic fluid. A natural consequence of this concept is that these phases, instead of competing with each other, might instead be intertwined, which means that different orders may arise with similar strengths.
The concept of electronic liquid crystal phases thus appears to be closely related to the existence of novel phases that exhibit a combination of topological order and symmetry breaking. This is the direction of work Professor Fradkin will pursue during his Center appointment. He plans to develop a theory of the interplay and phase transitions between topological order and symmetry breaking in condensed matter. Of particular interest is investigating the mechanisms that may bring about topological phases in three-dimensional systems and fully characterizing their edge states. He also plans to investigate the interplay and associated phase transitions from (and/or inside) topological phases to states with spontaneously broken symmetries.