This award supports fundamental theoretical research in condensed matter physics with the aim to advance understanding of electronic states of matter, the result of electrons in materials acting in concert to organize themselves to exhibit for example forms of magnetism, and superconductivity. The collective behavior of electrons in crystals is governed by the same principles of quantum mechanics which also determine the orbits of a single electron in a hydrogen atom. In a crystal, the quantum theory of many electrons implies the appearance of novel ways electrons organize themselves. The PI will investigate these novel types of order. Prominent among these is the appearance of high temperature superconductivity, the ability of electrons to conduct electricity without resistance even at temperatures above the boiling point of liquid nitrogen. Experiments have revealed additional types of order, some of which were predicted in the PI's early work, involving periodic modulations in the density of the electrons. In this project, the PI will study the interplay between multiple possible ways electrons can organize themselves. Research will be done in close contact with experimental research groups around the world. The existence of multiple kinds of order also opens up the possibility of a "quantum phase transition" in which there is a collective change in the quantum mechanical states of many electrons. The PI aims to relate the properties of quantum phase transitions to temperature dependencies of various properties observed in experiments. The theoretical research, in combination with experimental observations, is expected to lead to a deeper understanding of the structure of quantum matter. The understanding of new states of matter contributes fundamental knowledge that can lead to new technologies, for example new electronic devices and low loss power transmission. The research will be coupled with public lectures, articles in popular science journals, lectures at schools for advanced students. The research will be conducted by a group of students and postdoctoral fellows drawn from institutions around the world.
This award supports fundamental theoretical research on competing order, quantum phase transitions, and superconductivity. X-ray scattering experiments on the cuprate high temperature superconductors have exposed a regime where superconductivity competes with fluctuating 'charge' order, consistent with the PIs predictions. The PI has since developed a more comprehensive model of such behavior, and will investigate its consequences over wide regimes of temperatures, electron densities, and non-equilibrium time scales. Another set of experiments on the pnictide superconductors have clearly identified the importance of a quantum phase transition involving the onset of 'antiferromagnetic' order. The PI and collaborators have developed new field-theoretic and quantum Monte Carlo methods to investigate quantum phase transitions, and will use them to understand and predict physical properties near the critical point. The methods and analyses will also be applied to similar experimentally relevant issues in bilayer graphene, optical lattices of ultra-cold atoms, and to atomic systems strongly coupled to optical cavities. The research will lead to deeper insights into the phase structures of quantum systems with multiple possible ordering instabilities. New methods, analytic and numeric, are being developed to understand strongly-coupled quantum critical points, and these will help understand the regimes of quantum criticality found in numerous quantum materials. A unified understanding is expected for many classes of quantum materials, in close contact with many experimental studies. The research will be coupled with public lectures, articles in popular science journals, and lectures at schools for advanced students. The research will be conducted by a group of students and postdoctoral fellows drawn from institutions around the world.
