CAREER: The Fate of Topology in Disordered Three-Dimensional Materials

【非技术摘要】该职业奖支持物质新拓扑状态研究的研究和教育活动。一些材料中的电子自组织成物质的拓扑状态，这些状态是通过应用理论凝聚态物理和拓扑学概念融合而形成的新思想而预测存在的。拓扑学是数学的一个分支，描述物体在变形、扭曲和弯曲下保持不变的特性。这些状态的存在导致了有趣的量子力学特性，这些特性不受材料微小变化的影响。无耗散导电通道和块状绝缘体在其表面和边缘被基本金属态自发覆盖是拓扑材料的有趣特征之一。它们在电子学、自旋电子学和量子计算机领域的未来技术应用前景广阔。然而，所有的材料都有缺陷、杂质和缺陷，统称为无序。本研究项目将聚焦于三维材料中无序与拓扑的相互作用。拓扑材料的性质对无序不敏感，但并非免疫。该项目旨在促进对拓扑材料中无序影响的理解，并确定在电子设备、量子计算机和其他技术中健壮和实际应用的适当协议。为了发展一支具有国际竞争力的技术队伍，教育下一代科学家至关重要。首席研究员将通过建立一个强大的指导计划来帮助实现这一目标，该计划包括K-12学生、本科生、研究生以及博士后学者。PI将通过研究和接触工业工作机会，为研究生和博士后提供专业发展经验。最后，PI将开发强大的开源科学软件，这些软件将免费提供，以便研究无序拓扑材料。技术摘要：该职业奖支持理论凝聚态物理的研究和教育，重点关注物质的三维量子相中的无序、强相关和拓扑的相互作用。从低损耗电子到量子计算机，拓扑材料在未来的技术应用中具有很大的前景。然而，所有材料都含有无序性，因此确定哪些有用的拓扑性质在远离理想清洁极限的情况下保持鲁棒性是至关重要的。因此，这项研究活动的目标有三个：(1)确定无序的非摄动效应是否会破坏将三维拓扑绝缘体和平凡绝缘体分离成金属相的量子临界点。(2)开发一种有效的数值方法来计算非线性光学响应，以检测和表征三维材料的拓扑特性。(3)确定无序是否影响强相关材料中突发性拓扑带结构的形成。PI将采用大规模数值计算，利用核多项式方法和对角化技术来有效地模拟没有平移对称性的大型晶格模型。这项研究活动利用了统计物理学、拓扑场理论、临界现象和计算物理学的交叉施肥思想。这项研究的最终目标是确定无序如何从根本上改变物质的无间隙拓扑相。计划中的基础研究将有助于建立理论框架，以评估无序对物质无间隙拓扑相的影响，这将量化技术应用所需的纯度水平。PI的教育计划旨在通过积极的指导、研究机会、与行业合作伙伴的会议以及开发开源科学软件来培养具有竞争力的技术劳动力。特别是，PI的教育活动将集中在三个主要领域：(1)PI将通过指导将研究与教学结合起来，以改善K-12学生，本科生，研究生以及博士后学者的STEM教育。(2) PI将通过研究接触和行业交流相结合，促进研究生的专业发展，从而培养一支多元化、具有竞争力的劳动力队伍。(3) PI将开发一个开源的科学软件包来模拟无序量子系统，该软件包将公开提供，以增强研究和教育的基础设施。这个奖项反映了NSF的法定任务,通过评价被认为是值得支持使用基础的知识价值和广泛影响审查标准。

NONTECHNICAL ABSTRACTThis CAREER award supports research and educational activities in the study of new topological states of matter. Electrons in some materials self-organize into topological states of matter which are predicted to exist from the application of new ideas forged from the fusion of concepts from theoretical condensed matter physics and topology, the branch of mathematics that describes the properties of objects that remain unchanged under deformation, twisting, and bending. The existence of these states leads to intriguing quantum mechanical properties that are unaffected by small changes in the material. Dissipationless electrical conduction channels and bulk insulators that are spontaneously covered by essential metallic states at their surfaces and edges are among the interesting features of topological materials. They hold promise for future technological application in electronics, spintronics and quantum computers. However, all materials have imperfections, impurities, and defects, together referred to as disorder. This research project will focus on the interplay of disorder and topology in three-dimensional materials. The properties of topological materials are insensitive to disorder, but they are not immune. This project is aimed to advance understanding of the effects of disorder in topological materials and to determine the appropriate protocols for robust and practical applications in electronic devices, quantum computers and other technologies.In order to develop an internationally competitive technical workforce, it is essential to educate the next generation of scientists. The principal investigator will help achieve this goal by developing a strong mentorship program that includes students that are K-12, undergraduate, and graduate, as well as postdoctoral scholars. The PI will provide graduate students and postdocs with professional development experiences through research and exposure to industrial job opportunities. Lastly, the PI will develop powerful open source scientific software that will be made freely accessible in order to study disordered topological materials.TECHNICAL ABSTRACTThis CAREER award supports research and education in theoretical condensed matter physics focusing on the interplay of disorder, strong correlation, and topology in three-dimensional quantum phases of matter. Topological materials hold great promise for future technological applications ranging from low-loss electronics to quantum computers. However, all materials contain disorder and it is therefore essential to ascertain what useful topological properties remain robust away from the idealized clean limit. Therefore, the objectives of this research activity are threefold: (1) Determine if non-perturbative effects of disorder generically destabilize the quantum critical point that separates three-dimensional topological and trivial insulators into a metallic phase. (2) Develop an efficient numerical method to compute nonlinear optical responses to detect and characterize topological properties of three-dimensional materials. (3) Determine if disorder affects the formation of emergent topological band structures in strongly correlated materials. The PI will employ large scale numerical calculations that utilize the kernel polynomial method and diagonalization techniques to efficiently simulate large lattice models without translational symmetry. This research activity utilizes a cross fertilization of ideas from statistical physics, topological field theories, critical phenomena, and computational physics. The ultimate goal of this research is to determine how disorder fundamentally alters gapless topological phases of matter. The planned fundamental research will help to establish the theoretical framework for evaluating the impact of disorder on gapless topological phases of matter, which will quantify the required levels of purity for use in technological applications. The PI’s education plan aims to develop a competitive technical workforce through active mentorship, research opportunities, meeting with industry partners, and developing open source scientific software. In particular, the PI’s education activities will focus on three main areas: (1) The PI will integrate research with teaching through mentorship to improve STEM education for students from K-12, undergraduates, and graduates, as well as postdoctoral scholars. (2) The PI will develop a diverse, competitive workforce by fostering graduate student professional development through a combination of research exposure and industry exchanges. (3) The PI will develop an open source scientific software package to simulate disordered quantum systems that is made publicly available to enhance the infrastructure for research and education.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.