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

职业：无序三维材料中拓扑的命运

• 批准号: 1941569
• 负责人: Jedediah Pixley
• 金额: $ 61.53万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1941569&HistoricalAwards=false
• 关键词: CAREER; Fate; Topology; Disordered; Three

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.

非技术摘要这个职业奖支持研究和教育活动的研究新的拓扑状态的物质。某些材料中的电子自组织成物质的拓扑状态，这种状态是通过应用理论凝聚态物理学和拓扑学的概念融合而形成的新思想而预测存在的，拓扑学是数学的分支，描述了物体在变形、扭曲和弯曲下保持不变的性质。这些状态的存在导致了有趣的量子力学性质，这些性质不受材料中微小变化的影响。无耗散的导电通道和体绝缘体在其表面和边缘自发地被基本金属态覆盖是拓扑材料的有趣特征之一。它们为电子学、自旋电子学和量子计算机的未来技术应用带来了希望。然而，所有材料都有不完美、杂质和缺陷，统称为无序。本研究计画将着重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，但它们不是免疫的。该项目旨在促进对拓扑材料中无序效应的理解，并确定电子设备、量子计算机和其他技术中稳健和实际应用的适当协议。为了培养具有国际竞争力的技术人才，必须培养下一代科学家。首席研究员将通过制定一个强大的导师计划来帮助实现这一目标，该计划包括K-12，本科和研究生以及博士后学者的学生。PI将通过研究和接触工业就业机会为研究生和博士后提供专业发展经验。最后，PI将开发功能强大的开源科学软件，供免费访问，以研究无序拓扑材料。技术摘要该职业奖项支持理论凝聚态物理学的研究和教育，重点关注无序、强相关性和拓扑结构的相互作用。物质的三维量子相。 拓扑材料在未来的技术应用中具有很大的潜力，从低损耗电子到量子计算机。然而，所有的材料都包含无序，因此必须确定哪些有用的拓扑性质在远离理想化的干净极限的情况下仍然是稳健的。因此，这项研究活动的目标有三个方面：（1）确定无序的非微扰效应是否会使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不稳定。(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性质。(3)确定无序是否影响强关联材料中涌现拓扑能带结构的形成。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有效地模拟没有平移对称的大型晶格模型。这项研究活动利用了统计物理学，拓扑场论，临界现象和计算物理学的思想交叉施肥。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导师制，研究机会，与行业合作伙伴会面以及开发开源科学软件来培养具有竞争力的技术人才。特别是，PI的教育活动将集中在三个主要领域：（1）PI将通过导师制将研究与教学结合起来，以改善K-12学生，本科生和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的结合，培养研究生的专业发展，培养一支多元化，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，以加强研究和教育的基础设施。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Long-ranged spectral correlations in eigenstate phases

• DOI: 10.1088/1751-8121/ad1342
• 发表时间: 2022-07
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: A. Prakash;Mahaveer Prasad;J. Pixley;M. Kulkarni

Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone

在单个无序外尔锥的精确数值模拟中避免了量子临界

• DOI: 10.1103/physrevb.102.100201
• 发表时间: 2020
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Wilson, Justin H.;Huse, David A.;Das Sarma, S.;Pixley, J. H.
• 通讯作者: Pixley, J. H.

Universal spectral form factor for many-body localization

• DOI: 10.1103/physrevresearch.3.l012019
• 发表时间: 2020-08
• 期刊: arXiv: Disordered Systems and Neural Networks
• 作者: A. Prakash;J. Pixley;M. Kulkarni

Aubry-André Anderson model: Magnetic impurities coupled to a fractal spectrum

Aubry-André Anderson 模型：磁性杂质与分形谱的耦合

• DOI: 10.1103/physrevb.106.165123
• 发表时间: 2022
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Wu, Ang-Kun;Bauernfeind, Daniel;Cao, Xiaodong;Gopalakrishnan, Sarang;Ingersent, Kevin;Pixley, J. H.
• 通讯作者: Pixley, J. H.

Berry phase manipulation in ultrathin SrRuO3 films

• DOI: 10.1103/physrevb.102.220406
• 发表时间: 2019-07
• 期刊: arXiv: Strongly Correlated Electrons
• 作者: Liang Wu;Fangdi Wen;Yixing Fu;Justin H. Wilson;Xiaoran Liu;Yujun Zhang;D. Vasiukov;M. Kareev;J. Pixley;J. Chakhalian