CAREER: "Geometry, topology and symmetry in strongly correlated materials"

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education aimed to study the properties of certain materials called topological phases. These are states of matter which unlike most others have physical properties that are robust and are not affected by deformation and impurities. This leads to the possibility that some topological phases can be profitably used to store information and manipulate its flow in ways that are not possible in today's computers. Most kinds of materials that might lend themselves to these applications have so far been engineered in conditions which are quite hard to achieve under ordinary conditions; they require very high magnetic fields and very low temperatures. The PI will perform theoretical research aimed to understand better the physics of the materials that host topological phases of electrons and to explore the conditions that most favor the realization of topological phases in the absence of large magnetic fields. Robust phenomena similar to those that occur in electronic topological phases are also predicted to occur in systems which are acted on by a periodic external perturbation. The PI aims to understand these better and to classify the types of behavior that are possible. This research may contribute to eventual useful applications in metrology and in computation, and may help develop and improve open source quantum many-body computer programs. It could also lead to the development of new photonic devices. The PI will work with existing outreach programs at University of California, Los Angeles to introduce new experiments to the pre-collegiate curriculum. The PI will tap into an existing "Research Experience for Undergraduates" program to involve undergraduate students in research and build interest in physics among female students through the Clare Booth Luce foundation. The PI will continue development of course materials on topological phenomena and also help in dissemination of new ideas through introductory talks and a journal club. TECHNICAL SUMMARY This CAREER award supports theoretical research and education on strongly correlated systems focusing on the interplay among geometry, symmetry and topology. Topological phases lie outside the conventional paradigm of organizing phases by symmetry; nevertheless, they hold potential for enabling new device technologies and realizing quantum computation by virtue of their novel electronic properties. To advance understanding of topological phases, the PI will focus on the following thrusts: 1.) Developing a unified theory of the fractional quantum Hall effect and fractional Chern insulators. By incorporating aspects of the quantum geometry of the single particle Hilbert space in these systems, the PI proposes to design and develop new analytic and numerical tools which should aid the search for more experimentally accessible realizations of quantum Hall phenomena. 2.) Investigating the role of crystal symmetries in topological phenomena. Using topological arguments, the PI plans to improve constraints on symmetry enforced degeneracies and complete the classification of short-range entangled topological states with crystal symmetries. 3.) Exploring topological phenomena in periodically driven systems. The PI will aim to characterize these topologically robust phenomena, study the effects of interactions, the physical consequences of the classification, and connect these with experiments. The PI's education and outreach activities will promote diversity and improve science education at the elementary, undergraduate and graduate levels. The PI will work with existing outreach programs at the University of California, Los Angeles to introduce new experiments to the pre-collegiate curriculum. The PI will involve undergraduates in summer research programs through an existing "Research Experience for Undergraduates" program and build interest in physics among female students through the Clare Booth Luce foundation. The PI will continue developing course materials on topological phenomena. New developments in ongoing research will be disseminated through introductory talks and a journal club.