Topological Phases and Correlation Phenomena in Complex Materials

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on new kinds of solid materials and the surprising phenomena that emerge from the repulsion between their electrons. Idealized free electrons that interact with the positive nuclei of the solid but not with each other can already give surprising effects: the differences between metals, electrical insulators, and semiconductors can already be understood at this free-electron level. One part of the proposed work is concerned with newly discovered materials in topological states that can be analyzed using the branch of mathematics known as topology. Some topological phases can be understood in terms of free electrons, while others require strong interactions between the electrons. The PI will investigate both kinds of topological phases. Both can support atomically thin conducting layers at the surface of a bulk insulator, which have potential for technological applications. The PI will pursue a major new research direction to understand topological effects in metals and in optical properties such as light reflection and transmission, building on recent success in insulators and for transport properties such as conductivity. Interactions between the electrons are crucial in allowing systems to reach the steady state of thermal equilibrium, or put another way, to have a well-defined temperature. The second focus of the research is to understand quantum matter far from the steady state of equilibrium, like certain semiconductor devices. There are indications that numerous new states and phenomena emerge when quantum effects are particularly strong. This award also supports broader impacts with a common goal. This project will contribute to the training of graduate students in important fields of condensed matter physics, some of which have the potential to yield practical technologies. The PI will continue mentoring at the undergraduate, graduate, and postdoctoral levels with special attention to members of groups currently underrepresented in the physical sciences, including service as physics faculty advisor to a new UC Berkeley program. An accessible book on topological phases of matter, including the quantum Hall effect, spin liquids, and topological insulators, will be co-authored with an international collaborator. Occasional lectures to the lay public and K-12 classes will help spread enthusiasm for physics and materials science. The PI will continue to organize conferences and a focused seminar at Berkeley in order to propagate research developments, and will also seek to contribute to the condensed matter community through other forms of service. TECHNICAL SUMMARY This award supports theoretical research and education on new kinds of order that emerge has a consequence of interactions in quantum systems. Strongly interacting quantum systems can exhibit new kinds of order and show many different kinds of temporal evolution. The research has three thrusts on understanding: 1. how the same geometric properties that underlie topological phases in gapped systems have observable consequences in gapless systems (metals) ranging from free-electron band metals to strongly correlated states arising in high magnetic fields. 2. quantum dynamics in one dimension in both translation-invariant systems and disordered systems through a combination of numerical matrix-product-state methods and analytic theory. The two main goals are to understand anomalous transport in strongly correlated, translation-invariant, non-integrable models and to develop connections between many-body localization, entanglement, and quantum chaos. 3. how fractional particles such as Majorana fermions modify non-equilibrium dynamics in topological phases. Research on these projects involves a combination of advanced analytical and numerical methods and will impact many areas of condensed matter physics, including experiments. This award also supports broader impacts with a common goal. This project will contribute to the training of graduate students in important fields of condensed matter physics, some of which have the potential to yield practical technologies. The PI will continue mentoring at the undergraduate, graduate, and postdoctoral levels with special attention to members of groups currently underrepresented in the physical sciences, including service as physics faculty advisor to a new UC Berkeley program. An accessible book on topological phases of matter, including the quantum Hall effect, spin liquids, and topological insulators, will be co-authored with an international collaborator. Occasional lectures to the lay public and K-12 classes will help spread enthusiasm for physics and materials science. The PI will continue to organize conferences and a focused seminar at Berkeley in order to propagate research developments, and will also seek to contribute to the condensed matter community through other forms of service.