This CAREER award supports theoretical research on the interplay between superconductivity, quantum liquid crystals, and topological phases. The PI aims to understand the interplay among multiple instabilities, seeing it as a key challenge to unlock the mysteries of strongly correlated quantum materials. The research is motivated by and based on experiments. It will involve computational and analytical approaches.
To address the interplay between superconductivity and quantum liquid crystal order, the PI will develop and use new theoretical measures for quantifying different broken spatial symmetry in nanoscale electronic patterns observed in disordered correlated systems. Experimental resolution is increasing and experiments reveal more patterns of this sort in many correlated materials. The PI's theoretical framework will provide a way to interpret new experiments. With the new measure, the PI will address the significance of local quantum liquid crystal physics in high Tc superconductors. She will develop tools to test signatures of quantum criticality inside the superconducting phase. To address the interplay between topological phases and the other two orders, the PI will develop new measures to distinguish different topological phases, that are applicable at finite temperatures. In parallel, the PI will continue the effort to identify signatures of abelian and nonabelian fractional statistics which are the best presently known indicators of toplogical phases. Finally, the PI will investigate two cases of the interplay among all three kinds of order: the ruthenate family and even-denominator-filling quantum Hall devices.
The educational component of this award will impact three relevant groups: undergraduate and graduate students in Physics and Applied Physics Departments at Cornell University, K-12 students nation-wide, and middle school girls in New York state. For Cornell students, the PI will develop "Scientific Science Communication" module to equip students with scientific writing and presentation skills. The module will become a permanent component of a traditional laboratory course for undergraduate and graduate students. With assistance from the Cornell Center for Materials Research, the PI will develop an educational kit "amazing liquid crystals", in order to demonstrate the diversity of emergent phenomena underlying everyday technology to K-12 students. The PI will partner with the Cornell chapter of the "Expand Your Horizons" program and introduce a cyber community aspect to the program to encourage interest in science among female students.
NONTECHNICAL SUMMARY
This CAREER award supports theoretical research on materials with emergent states of matter that arise from electrons that interact strongly with each other. Electrons are governed by the rules of quantum mechanics. Materials composed of many strongly interacting electrons display new states of matter, such as superconductivity. At sufficiently low temperature, electrons can collectively join together in the same quantum mechanical state, a superconducting state that can conduct electricity without dissipation. Other states of matter are possible. It is possible that a material is close to exhibiting more than one state of matter. These states may compete with each other leading to unusual properties in materials that lie outside the textbooks. This research project will use theory and computation to explore the interplay among three states of matter, superconductivity, quantum liquid crystal order in which electrons organize themselves in such a way that they have properties that have both liquid-like and crystal-like attributes, and topological order. Topological order is an emerging concept that connects the structure of a quantum mechanical state of many particles to more familiar concepts of the distinct ways particles organize themselves into states of matter. The interplay among these states may be carried out in materials like the high temperature superconductors and electrons in a high magnetic field that are confined to a plane in artificial structures made of semiconductor materials. The PI will seek to discover principles and concepts to describe the interplay among these states based on experimental findings. The goal is to develop a comprehensive theoretical framework combining analytical and computational approaches.
The educational component of this award will impact three relevant groups: undergraduate and graduate students in Physics and Applied Physics Departments at Cornell University, K-12 students nation-wide, and middle school girls in New York state. For Cornell students, the PI will develop "Scientific Science Communication" module to equip students with scientific writing and presentation skills. The module will become a permanent component of a traditional laboratory course for undergraduate and graduate students. With assistance from the Cornell Center for Materials Research, the PI will develop an educational kit "amazing liquid crystals", in order to demonstrate the diversity of emergent phenomena underlying everyday technology to K-12 students. The PI will partner with the Cornell chapter of the "Expand Your Horizons" program and introduce a cyber community aspect to the program to encourage interest in science among female students.
