****Technical Abstract**** "Topological Insulation" represents a new functionality whereby a specific inversion in the order of the energy bands in a 3D bulk insulator necessitates that the corresponding 2D surface would be metallic, with linearly dispersed crossing surface bands. Most remarkably, the ensuing surface states are spin-polarized and resilient to any passivation that respects the underlying symmetry. Unfortunately, in the absence of predictive "design principles", it has proven difficult to guide synthesis towards those materials in which this remarkable functionality would live. Indeed, the handful of known TI materials tend to be high-atomic number materials, thus not only being narrow-gap semiconductors, but also prone to structural defects that produce free carriers which obscure the TI-ness. We find that in addition to the band inversion necessitated for these, "Type1 TI's", there are other patterns of band inversion leading to different degrees of resilience to surface passivation. Such yet undiscovered cases, called here TI-2, as well as Band-Inversion (BI) of types 1 and 2 (BI-1, BI-2) could exist in a far wider range of materials, including wide gap insulators and semiconductors. We have developed theoretically calculable "Design Principles" (metrics of TI-ness) which we will apply, via first-principles electronic structure theory, to a wide range of both existing, and "designed" materials, screening for the specific patterns that would lead to TI-1, TI-2, BI-1 and BI-2 behaviors. Close integration with synthesis and ARPES experiments would lead to next-generation wide gap, light element TI's and BI's that would dramatically broaden the scope and understanding of surface electronic structure of new types of topological and band-inverted materials, providing a new paradigm for the design of conductive surfaces controlled by bulk properties.
Most high technologies are based on unique functionalities (conductivity, magnetism) that "live" in certain, specific materials and no others. Identifying, (out of an astronomic number of possibilities) those materials likely to have a specific functionality is a generally unsolved problem in material research. This work offers a general strategy around this problem. It focuses on a newly discovered functionality- a single material having a conducting surface but an insulating interior, a property called "Topological Insulation" (TI). By combining a calculable "metric" (based on quantum theory of matter) that guesses if a material is likely to be a TI or not, with laboratory synthesis and synchrotron measurement, we offer to identify hitherto unknown new materials that have such prescribed properties. Graduate students and post-doctoral researchers will be supported under this grant, and will receive training in broad aspects of materials theory, synthesis, and characterization, as well as communication and leadership skills.
This award is funded by the Division of Materials Research (DMR) and the Division of Mathematical Sciences (DMS).
