Emerging Topological Quantum Phases in Proximity-Coupled Nanostructures and Cold Atom Systems

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NONTECHNICAL SUMMARYThis award supports theoretical and computational research, and education aimed to design topological states in hybrid materials structures on the nanoscale and in systems of atoms trapped by light close to the absolute zero of temperature. Topological states are quantum mechanical states of many particles, usually electrons in materials or very cold atoms, that are characterized by properties that are peculiarly unchanged by deformations and imperfections of the system. It may be possible to harness topological states for applications in advanced communication, sensing, and quantum information technologies. Theoretical work has predicted different kinds of topological phases. Some are difficult to find in known materials. The PI will explore a different avenue, designing nanoscale structures of materials to engineer a predicted quantum state. Fhe PI aims to provide a detailed theoretical characterization of systems supporting topological quantum phases based on realistic modeling of solid state hybrid nanostructures and ultra-cold atom systems. The result will be guidance for experimental efforts in these areas and will contribute to the knowledgebase for engineering topological quantum states and developing new applications.The PI aims to investigate a series of basic science problems related to the realization and detection of topological quantum phases in solid state and cold atom systems. This project will involve in part the development of modular software that will be integrated into educational activities of the project. The research is focused on enhancing understanding of effects induced by close proximity of one part of a system to another in hybrid nanostructures and on characterizing the effects in solid-state heterostructures and cold-atom systems that arise as a consequence of strong interactions among electrons or atoms and lead to different kinds of topological quantum states. This award also supports graduate and undergraduate student training in a broad range of theoretical condensed matter techniques. A project-oriented peer mentoring program aimed to attract students into pursuing theoretical condensed matter research will also provide an educational resource that is expected to increase the success of underrepresented students of lower socio-economic status in science and engineering by effectively training them to exploit the critical connection between science and mathematics and by providing them with the opportunity to acquire useful computer programing and software development skills. TECHNICAL SUMMARYThis award supports theoretical and computational research, and education aimed to advance the understanding of topological quantum phases by bridging the gap between theoretical predictions based on minimal models and the complex phenomenology of real nanostructures under experimental conditions. This project focusses on characterizing the proximity effects that govern the low-energy physics of hybrid nanostructures and on carefully incorporating strong correlation effects. Specifically, the PI aims to: i) Identify optimal architectures for the realization, detection, and controlled manipulation ofMajorana fermions in solid state hybrid structures through realistic modeling of semiconductor nanowires and quantum dot arrays proximity-coupled to superconductors.ii.) Investigate emergent quantum states in topological insulator structures by developing a theory of proximity-induced phenomena in topological-insulator-based multilayer heterotructures and at interfaces between topological insulators and strongly correlated materials.iii.) Investigate quantum phases characterized by nontrivial topological properties in cold-atom systems by determining the effects of smooth confinement, exotic light-induced spin-orbit coupling, and strong many-body interactions.This research will provide firm guidance for the experimental efforts in these areas and will contribute to the knowledgebase for engineering topological quantum states and developing new applications.This award also supports graduate and undergraduate student training in a broad range of theoretical condensed matter techniques. A project-oriented peer mentoring program aimed to attract students into pursuing theoretical condensed matter research will also provide an educational resource that is expected to increase the success of underrepresented students of lower socio-economic status in science and engineering by effectively training them to exploit the critical connection between science and mathematics and by providing them with the opportunity to acquire useful computer programing and software development skills.