CAREER:Topological Crystalline Insulators and Semimetals: Beyond the Bulk-Edge Correspondence

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education on newly discovered topological phases of matter. Historically, phases of matter have been classified by the presence/absence of a local property, for example, a magnetic moment or arrangement of atoms in a solid vs a liquid. Topological phases defy this paradigm because they cannot be detected by any local probe. Consequently, their properties are robust to local perturbations, i.e., dirt that is inevitably present in any real device. Topological insulators, which have surfaces and edges that are metallic covering an insulating bulk, provide an important example. The surface of a topological insulator can conduct electricity, but, unlike an ordinary metal, the conductivity of the metallic surface does not decrease with disorder. This robust conductivity makes topological insulators promising for technological applications, including spintronics and quantum computing. The PI will examine topological materials with symmetry. Generically, crystals exhibit many symmetries. Because of symmetry, the structure of a crystal will look identical under specific rotations or perhaps, when viewed in a mirror. Recently, it has become clear that some materials that were not previously regarded as "topological" can also exhibit robust conducting states as long as the symmetry is preserved in the experiment. The PI aims to figure out how to detect and utilize the robust conducting states of these materials with symmetry. Mathematical and numerical modeling will be used to predict under what conditions robust conducting states will be present. The impact of the proposed research will be to increase the number of materials that can be used in devices intended for topological insulators. An important aspect of this project is an education plan for high school, undergraduate, and graduate students that includes specific outreach to women. For the high school and undergraduate students, the PI will utilize the existing infrastructure provided by the Women in Science and Engineering program at Stony Brook University to teach mini research modules and organize networking and mentoring events. For graduate students, the PI will develop a class on topological materials that incorporates professional development and will also rejuvenate the Women in Physics and Astronomy group. The overarching goal is to educate and diversify the future workforce in science and engineering. TECHNICAL SUMMARY This CAREER award supports research on the bulk-edge and bulk-defect correspondence for topological crystalline insulators and semimetals together with related education activities. The recent developments of symmetry indicators and elementary band representations have defined a new era in the prediction and classification of topological band structures. However, the bulk diagnosis of a topological crystalline phase does not guarantee a gapless surface state, and the surface signatures have lagged behind the bulk classification. Since, traditionally, topological phases are detected by their surface states, this presents a problem for the experimental diagnosis of newly discovered topological materials. The proposed work will address this problem by developing both symmetry classifications and experimental signatures of topological crystalline insulators and semimetals. Specifically, the research will focus on the following two classes of topological band structures: 1) Surface states of topological semimetals: crystal symmetry can protect non-chiral degenerate points that exhibit bulk topological invariants, but their surface signatures have never been studied. The proposed work will determine the conditions under which gapless surface and hinge Fermi arcs are topologically protected. 2) Defect modes of higher order topological insulators: the proposed work will establish a defect classification for higher order topological insulators. Bulk defect modes and surface step edges will provide more robust experimental signatures than corner states because they do not require cleaving a crystal in a particular way. These results will be crucial for future measurements of topological materials and device applications. The project integrates research and education through an education plan for high schoolers, undergraduates, and graduate students with outreach to women in science and engineering. The plan will be accomplished in three parts 1) utilizing the existing infrastructure of the Women in Science and Engineering program at Stony Brook to design a research module for high school and undergraduate women and to host a networking panel; 2) designing a graduate course called Topological Insulators and Semimetals that will have a built-in professional development component; and 3) rejuvenating the Women in Physics and Astronomy group at Stony Brook University, with the long term goal of increasing the retention rate of female students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.