CAREER:Topological and Strongly Correlated Electronic Phases

University Of Texas At Austin, Austin TX

Investigators

Abstract

TECHNICAL SUMMARY This CAREER award supports an integrated program of research and education in the theory of topological and strongly correlated electronic phases of matter. Topological phases constitute a new and rapidly broadening frontier in condensed matter physics. Their robustness against imperfections and disorder make them especially promising for certain applications. The PI proposes to use a combination of analytical and numerical methods, with an emphasis on the former, to study three classes of correlated electronic states of matter: 1. Strongly interacting one-dimensional systems at zero and non-zero temperature. Particular emphasis will be placed on the regime of highly thermalized spin degrees of freedom. Various aspects of the so-called spin-incoherent Luttinger liquid will be studied. 2. Finite size effects in single and multi-layer fractional quantum Hall systems. Phases that realize non-Abelian quasi-particle statistics will receive the most attention and effort will be placed on developing proposals to experimentally identify their existence. 3. Quantum liquids and topological insulators. The PI proposes to study the role of spin-orbit coupling in the realization and stabilization of different types of matter exhibiting topological order. The educational focus of this proposal seeks to advance discovery, promote teaching in the sciences, broaden participation of under represented groups, and inform the broader public about the central role science plays in the well being of our society. These goals will be accomplished in a number of ways. Among them are: + Outreach to high school students, particularly those from historically underrepresented groups. The PI will visit local Austin-area high schools with large Hispanic/Latino populations to interact with students and teachers. + Mentoring of female scientists. The PI will participate in the University of Texas "Alice in Wonderland" summer program for talented female high school students interested in physics. + Increasing the number of K-12 science teachers in Texas. The PI is actively involved in recruiting undergraduate students to a science education major. + Undergraduate participation in research. The PI will supervise undergraduate students as they pursue research to provide them with a meaningful taste of life as a scientist. + Partnership with local Austin high-tech industry. The PI will enhance contact with the private sector through collaborations with their scientists. + Outreach to the broader public at Texas Natural Science Center. The PI plans public lectures to present research results in an exciting and informative way. NON-TECHNICAL SUMMARY This CAREER award supports an integrated program of research and education in the theory of new states of matter. Atoms organize themselves in distinctly different ways in different materials. The carbon atoms in diamond are self-arranged differently than those in graphite giving rise to distinctly different properties. The precise mathematical concept of symmetry based on the how the crystal can be flipped, rotated, or moved in such a way that the crystal looks the same enables the classification of phases. This classification is sufficiently general to encompass crystals composed of atoms, as well as the phases of electrons in materials, for example magnetism or quantum mechanical states where electrons themselves organize into a crystal. The study of phases of electrons trapped in a plane and exposed to a strong magnetic field, concisely known as the quantum Hall effects, has expanded the concept of order. This classification is related to a branch of mathematics known as topology and the phases are said to exhibit topological order. Topological phases are robust against imperfections, deformations, and impurities. The PI will use advanced theoretical methods to study topological phases and how they arise. The PI will also study materials and systems which contain electrons that interact strongly with each other leading to complex correlations in their motions. The manipulation of topological phases may form the basis of new paradigms in computation and may contribute to future information technologies. The educational focus of this proposal seeks to advance discovery, promote teaching in the sciences, broaden participation of under represented groups, and inform the broader public about the central role science plays in the well being of our society. These goals will be accomplished in a number of ways. A few of them are: + Outreach to high school students, particularly those from historically underrepresented groups. The PI will visit local Austin-area high schools with large Hispanic/Latino populations to interact with students and teachers. + Mentoring of female scientists. The PI will participate in the University of Texas "Alice in Wonderland" summer program for talented female high school students interested in physics. + Increasing the number of K-12 science teachers in Texas. The PI is actively involved in recruiting undergraduate students to a science education major. + Undergraduate participation in research. The PI will supervise undergraduate students as they pursue research to provide them with a meaningful taste of life as a scientist. + Partnership with local Austin high-tech industry. The PI will enhance contact with the private sector through collaborations with their scientists. + Outreach to the broader public at Texas Natural Science Center. The PI plans public lectures to present research results in an exciting and informative way.