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

该奖项支持理论和计算研究，以及旨在设计纳米级混合材料结构拓扑状态的教育，以及在接近绝对零度的温度下被光捕获的原子系统。拓扑态是许多粒子的量子力学态，通常是材料中的电子或非常冷的原子，其特征是由于系统的变形和缺陷而特别不变。在先进的通信、传感和量子信息技术中，利用拓扑状态的应用是可能的。理论工作预测了不同类型的拓扑相。有些在已知材料中很难找到。PI将探索不同的途径，设计纳米级材料结构来设计预测的量子态。该项目旨在基于固体混合纳米结构和超冷原子系统的实际建模，提供支持拓扑量子相的系统的详细理论表征。该结果将指导这些领域的实验工作，并将为工程拓扑量子态和开发新应用贡献知识库。该项目旨在研究与固态和冷原子系统中拓扑量子相的实现和检测相关的一系列基础科学问题。该项目将部分涉及模块化软件的开发，该软件将集成到项目的教育活动中。研究的重点是加强对混合纳米结构中系统的一部分与另一部分的密切接触所引起的效应的理解，以及表征固态异质结构和冷原子系统中的效应，这些效应是由于电子或原子之间的强相互作用而产生的，并导致不同种类的拓扑量子态。该奖项还支持研究生和本科生在广泛的理论凝聚态技术的培训。一个以项目为导向的同伴指导计划旨在吸引学生从事凝聚态理论研究，它也将提供一种教育资源，通过有效地训练他们利用科学和数学之间的关键联系，并为他们提供获得有用的计算机编程和软件开发技能的机会，有望增加社会经济地位较低的学生在科学和工程领域的成功。该奖项支持理论和计算研究，以及旨在通过弥合基于最小模型的理论预测与实验条件下真实纳米结构的复杂现象学之间的差距，促进对拓扑量子相的理解的教育。本项目的重点是描述控制混合纳米结构低能物理的接近效应，并仔细结合强相关效应。具体来说，PI的目标是：i)通过半导体纳米线和量子点阵列的接近耦合超导体的现实建模，确定固态混合结构中马约拉纳费米子的实现，检测和控制操作的最佳架构。通过发展基于拓扑绝缘体的多层异质结构和拓扑绝缘体与强相关材料之间界面的邻近诱导现象理论，研究拓扑绝缘体结构中的涌现量子态。通过确定光滑约束、外来光诱导自旋轨道耦合和强多体相互作用的影响，研究冷原子系统中具有非平凡拓扑特性的量子相。该研究将为这些领域的实验工作提供坚实的指导，并将为工程拓扑量子态和开发新的应用提供知识库。该奖项还支持研究生和本科生在广泛的理论凝聚态技术的培训。一个以项目为导向的同伴指导计划旨在吸引学生从事凝聚态理论研究，它也将提供一种教育资源，通过有效地训练他们利用科学和数学之间的关键联系，并为他们提供获得有用的计算机编程和软件开发技能的机会，有望增加社会经济地位较低的学生在科学和工程领域的成功。

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.