CAREER: Topology, Symmetry and Disorder in Strongly Correlated Systems

University Of California-Irvine, Irvine CA

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports basic theoretical research on the self-organization of electrons in materials that are quantum mechanical phases of matter characterized by topological order. Experiments cannot distinguish among such phases by probing small pieces of the material, but instead must perform measurements that in effect probe the entire extent of a sample. This suggests that topological phases may be potent tools for storing and manipulating quantum-mechanical information. In contrast to familiar information storage technologies, information would be encoded globally in a topological phase and would be protected against the detrimental effects of material imperfections and other extrinsic sources of interference, that are generally confined to small regions. Implementing this intriguing idea to build a topological quantum computer is a major technical challenge, while understanding the behavior of these unusual phases of matter is a fundamental problem. This project approaches these goals from two directions. The first is to develop a systematic understanding of topological phases from the perspective of the symmetry of their crystalline host materials. This will enable the identification and classification of new topological phases, including 'semi-metals' intermediate between metals and semiconductors that may provide platforms for new quantum devices. The second direction is to understand the behavior of a simple quantum computer: a system of many interacting computer bits governed by the laws of quantum mechanics isolated from their surroundings. The PI will examine whether such systems can avoid evolving into a state of thermal equilibrium which could wash out their quantum information content. The PI aims to develop techniques to probe the unusual phases that result when such an equilibrium is evaded. In a fundamental sense, these quantum states resemble 'glasses' and appear to represent a fundamentally new type of system governed by quantum mechanics, with the potential for new and surprising behaviors and applications. Alongside these research goals, the PI will implement a comprehensive education and outreach plan. One effort will use thought-provoking experiments to expose middle school students - drawn predominantly from schools with a large proportion of students of low socio-economic status - to basic scientific questions. This will build in to existing outreach programs at the PI's institution, and go beyond them by providing materials and guidance for their teachers to duplicate such discovery activities in the classroom. The PI will develop new courses at the graduate and undergraduate levels and establish a journal club to acquaint graduate students with research literature. The project includes funding for graduate and undergraduate students, who will be actively mentored and given the opportunity to participate in both national and international scientific collaborations or conferences. The PI will also found a biennial summer school to prepare beginning graduate students in Southern California for research careers in condensed matter physics. The school will promote diversity by encouraging participation by nontraditional and minority students in the California State University system. TECHNICAL SUMMARY This CAREER award supports theoretical research into condensed matter systems where interactions among constituent particles lead to topological phases of matter. Such phases are potentially relevant to building decoherence-resistant topological qubits for quantum computers. The first thrust of the research activity will examine how crystalline symmetries delineate possible phases of matter, building on prior work by the PI and collaborators demonstrating the role of 'non-symmorphic' symmetries. Generalizing these ideas, the PI will study systems where spin-orbit and interelectron interactions lead to new phases. The PI will also examine how such symmetries lead to Landau-forbidden phase transitions, using simple exactly solvable models. Armed with these results, the P.I. will analyze the classification of interacting topological crystalline insulators. Finally, the novel transport properties of the semi-metals that emerge as a consequence of crystalline symmetries or accidental degeneracies between energy bands will be studied, with an emphasis on their connection to quantum anomalies. The second broad direction examines the response of topological phases to impurities. Three main problems will be addressed: (i) the development of new dynamical probes capable of discerning subtle effects of interactions on disordered, isolated topological systems; (ii) an analysis of the behavior of disordered chains of non-Abelian anyons to examine their potential for realizing novel many-body localized phases with low entanglement; and (iii) the possibility of granular phases in disordered quantum Hall systems, similar to analogous phases in dirty superconductors, which would represent an unusual form of topological matter. The P.I. will also implement a comprehensive education plan that integrates these research goals into outreach aimed at K-12 students, undergraduate and graduate research and mentoring, curricular and professional development of junior researchers. The project will also establish a biennial summer school to prepare beginning graduate students in Southern California for re-search careers in condensed matter physics.