Topological Materials Beyond Symmetry Indicators

About This Grant

NONTECHNICAL SUMMARY This award supports theoretical research and educational activities aimed at understanding topological materials. These materials are distinguished in having properties that remain unchanged when the material is reshaped or disturbed. Topological materials have robust, i.e. impervious to material imperfections or shape, metallic conduction on their surfaces and interfaces that hold promise for device applications. Recent theoretical work has revealed that topological materials are ubiquitous in nature. However, the analytic tools for efficiently identifying and classifying topological materials are applicable to only about half of the crystal arrangements of constituent atoms that occur in nature, and only in materials where electrons do not interact strongly. A unifying framework for understanding how these analytical tools relate to measurable properties of materials is also lacking. This project will focus on addressing this issue by exploiting mathematical connections between topology and symmetry as they apply in materials. The PI will develop new mathematical frameworks for describing the connection between symmetry in topology in solids and apply these to the discovery of new topological materials. Additionally, the PI will use symmetry to study how electron flow and crystal imperfections can reflect universal properties of topological materials. In addition to the research, this project supports the training and mentorship of graduate students and their preparation to join the nation's quantum workforce, as well as improved access to physics education and research. This project is expected to result in the development of software tools and databases to aid in the discovery of new topological materials, which will be made available to the wider physics and materials science communities. A major part of this research is directly applicable to ongoing work in experimental research laboratories. TECHNICAL SUMMARY This project is focused on the theoretical study of the interplay between topology and symmetry in topological materials. The discovery of topological materials has revolutionized condensed matter physics, and has promised transformative breakthroughs due to their robust transport properties, edge states, and exotic quasiparticle excitations. Developments over the past several years have shown that topological materials are ubiquitous in nature. The theory of topological quantum chemistry and symmetry-based indicators has given researchers new tools to quickly screen for nontrivial topology in weakly-correlated materials, based on the symmetry properties of electronic wavefunctions in momentum space. In spite of this tremendous progress, there are two major outstanding hurdles before the promise of harnessing topological effects can be realized: Symmetry indicators are not applicable to approximately half of the known crystal symmetry types, and a unifying framework connecting symmetry indicator invariants to experimental observables is not known. In this project, the PI will address these issues by: 1) Studying the hydrodynamics of topological crystalline insulators and their response to defects to identify observable consequences of nontrivial topology beyond the bulk boundary correspondence. Both hydrodynamic response and the response of the bulk and boundary to defects will be investigated; 2) Developing group-theoretic techniques to define extended symmetry indicators for topological insulators and superconductors applicable to chiral materials. Attention will be paid to incorporating internal symmetries such as sublattice and particle hole symmetries with spatial symmetries in a consistent framework. Additionally, the action of spatial symmetries on electron spin will be explored as an indicator of topology. In addition to the research, this project supports the training and mentorship of graduate students and their preparation to join the nation's quantum workforce, as well as improved access to physics education and research. This project is expected to result in the development of software tools and databases to aid in the discovery of new topological materials, which will be made available to the wider physics and materials science communities. A major part of this research is directly applicable to ongoing work in experimental research laboratories. 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.