CAREER: Topology and Geometry in Condensed Matter Systems

职业：凝聚态系统中的拓扑和几何

• 批准号: 1945058
• 负责人: Barry Bradlyn
• 金额: $ 53.27万
• 依托单位: University of Illinois at Urbana-Champaign
• 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: 2020-07-15 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1945058&HistoricalAwards=false
• 关键词: CAREER; Topology; Geometry; Condensed; Matter

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education in the rapidly developing field of topological materials. The discovery of topological phases of matter is one of the most transformative recent breakthroughs in condensed matter physics, revealing new conceptual surprises in established topics such as the phases of matter and the behavior of electrons in insulators. Mathematically, topology refers to a property that remains unchanged when a sample is distorted in some way. Topologically nontrivial materials exhibit metallic surface states that are present regardless of how dirty the system is. However, from a practical perspective, the promise of devices harnessing these topological effects remains--for the most part--unrealized, due both to the lack of tools for finding realistic topological systems and the need for an improved understanding of the response of topological systems to external probes.One tool that can be leveraged to address these issues is geometry. Geometry enters into the description of crystal symmetry (example: an equilateral triangle looks the same after rotation by 60 degrees) and places constraints on the behavior of materials in the presence of electromagnetic fields and strain. The focus of this research is to use the interplay of geometry and topology to develop new insights into topological materials. The PI will use symmetry principles to determine ways to characterize topological materials through their behavior in external fields. Additionally, the interplay between crystal symmetries and electron-electron interactions in topological materials will be investigated with the goal of enabling the discovery of the next generation of topological materials.A major part of this research is directly applicable to ongoing work in experimental research laboratories. This research is closely integrated into an education plan at the undergraduate and graduate levels involving 1) the development of an advanced-level graduate course on Berry phases and topology in electronic structure, which is not currently covered in detail in current course offerings, 2) mentoring of undergraduate students in research both over the summer and during the school year, and 3) an outreach plan using techniques from statistical physics to study online harassment, in order to demonstrate the applications of physics to data science.TECHNICAL SUMMARYThis CAREER award supports research into the interplay between crystal geometry and topological phenomena in order to develop a deeper understanding of quantum matter.The discovery of topological materials has revolutionized the understanding of quantum matter, demonstrating that not all insulators are created equal. The most striking experimental feature of topological materials is the existence of protected edge states, leading to protected non-dissipative conduction. However, topological materials also host remarkable bulk properties, such as non-dissipative transport coefficients, lack of localized electronic orbitals, and counterintuitive coupling to crystal geometry. The central goal of this award is to apply geometric data to compute previously unstudied properties of topological systems. This will be achieved through the study of1. Response as a probe of topology: geometric transport coefficients such as the Hall viscosity will be studied to elucidate the interplay between anisotropy, geometric, and hydrodynamic response in topological systems. The proposed work will also determine the connection between topology and nonlinear electromagnetic response in a variety of experimentally relevant systems.2. Role of symmetry in free-fermion band topology: the mathematical underpinnings of topological band theory will be extended in order better to understand the role of crystal symmetry in allowing for topologically nontrivial bands. Furthermore, symmetry principles will be applied to incommensurate and quasiperiodic structures to develop the theory of topological phases in quasiperiodic systems.3. Crystal symmetries in interacting topological systems: the constraints of crystal symmetries will be incorporated into the study of many-body topological phases, and the theory of band representations for the elementary excitations in correlated phases will be developed.This CAREER project will serve to provide a richer understanding of topological and strongly correlated phases of quantum matter. A major part of this research is directly applicable to ongoing work in experimental research laboratories. This research is closely integrated into an education plan at the undergraduate and graduate levels involving 1) the development of an advanced-level graduate course on Berry phases and topology in electronic structure, which is not currently covered in detail in current course offerings, 2) mentoring of undergraduate students in research both over the summer and during the school year, and 3) an outreach plan using techniques from statistical physics to study online harassment, in order to demonstrate the applications of physics to data science.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.

非技术总结这个职业奖项支持在快速发展的拓扑材料领域的理论研究和教育。物质拓扑相的发现是凝聚态物理学最具变革性的最新突破之一，揭示了物质相和绝缘体中电子行为等既定主题的新概念惊喜。从数学上讲，拓扑是指当样本以某种方式扭曲时保持不变的属性。在拓扑上，非平凡材料表现出金属表面状态，无论系统有多脏都存在。然而，从实践的角度来看，设备利用这些拓扑效应的前景仍然--在很大程度上--没有实现，这既是因为缺乏寻找现实拓扑系统的工具，也是因为需要更好地理解拓扑系统对外部问题的响应。可以利用的一个工具是几何。几何学进入对晶体对称性的描述(例如，等边三角形旋转60度后看起来相同)，并对材料在电磁场和应变存在下的行为施加约束。这项研究的重点是利用几何和拓扑的相互作用来发展对拓扑材料的新见解。PI将使用对称性原理来确定通过其在外部场中的行为来表征拓扑材料的方法。此外，还将研究拓扑材料中晶体对称性和电子-电子相互作用之间的相互作用，以期发现下一代拓扑材料。这项研究的主要部分直接适用于实验研究实验室正在进行的工作。这项研究紧密结合到本科生和研究生层面的教育计划中，涉及1)开发一门关于Berry相和电子结构拓扑学的高级研究生课程，目前的课程没有详细涉及这一课程；2)指导本科生在夏季和学年进行研究；以及3)使用统计物理学的技术研究在线骚扰的扩展计划，为了展示物理学在数据科学中的应用。技术总结这个职业奖支持对晶体几何和拓扑现象之间相互作用的研究，以加深对量子物质的理解。拓扑材料的发现彻底改变了对量子物质的理解，表明并不是所有的绝缘体都是生而平等的。拓扑材料最显著的实验特征是存在受保护的边态，这导致了受保护的非耗散导电。然而，拓扑材料也具有显著的整体性质，如非耗散输运系数，缺乏定域电子轨道，以及与晶体几何形状的反直觉耦合。该奖项的中心目标是应用几何数据来计算以前没有研究过的拓扑系统的性质。这将通过研究1来实现。响应作为拓扑的探测者：我们将研究几何输运系数，如霍尔粘度，以阐明拓扑系统中各向异性、几何和流体动力响应之间的相互作用。所提出的工作还将确定各种实验相关系统中的拓扑和非线性电磁响应之间的联系。对称性在自由费米子带拓扑中的作用：拓扑带理论的数学基础将被扩展，以便更好地理解晶体对称性在允许拓扑上非平凡的带中的作用。此外，将对称性原理应用于无公度准周期结构，发展了准周期系统的拓扑相理论。相互作用拓扑系统中的晶体对称性：晶体对称性的约束将被纳入到多体拓扑相的研究中，并将发展相关相中基本激发的能带表示理论。这一职业项目将有助于对量子物质的拓扑和强关联相有更丰富的理解。这项研究的主要部分直接适用于实验研究实验室正在进行的工作。这项研究被紧密地整合到本科生和研究生层面的教育计划中，涉及1)开发一门关于Berry阶段和电子结构拓扑学的高级研究生课程，目前的课程没有详细涉及这一点，2)指导本科生在夏季和学年进行研究，以及3)使用统计物理学的技术来研究在线骚扰，以展示物理学在数据科学中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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

Understanding the Use of Fauxtography on Social Media

了解仿照在社交媒体上的使用

• 发表时间: 2021
• 期刊: Proceedings of the International AAAI Conference on Weblogs and Social Media
• 作者: Wang, Yuping;Tahmasbi, Fatemeh;Blackburn, Jeremy;Bradlyn, Barry;De Cristofaro, Emiliano;Magerman, David;Zannettou, Savvas;Stringhini, Gianluca
• 通讯作者: Stringhini, Gianluca

Topological crystalline phases in a disordered inversion-symmetric chain

• DOI: 10.1103/physrevb.103.024205
• 发表时间: 2020-07
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Saavanth Velury;B. Bradlyn;T. Hughes

Cubic Hall viscosity in three-dimensional topological semimetals

• DOI: 10.1103/physrevresearch.3.l032068
• 发表时间: 2021-02
• 期刊: Physical Review Research
• 影响因子: 4.2
• 作者: I. Robredo;P. Rao;Fernando de Juan;A. Bergara;J. Mañes;A. Cortijo;M. Vergniory;B. Bradlyn

Failure of Topological Invariants in Strongly Correlated Matter

强相关物质中拓扑不变量的失效

• DOI: 10.1103/physrevlett.131.106601
• 发表时间: 2023
• 期刊: Physical Review Letters
• 影响因子: 8.6
• 作者: Zhao, Jinchao;Mai, Peizhi;Bradlyn, Barry;Phillips, Philip
• 通讯作者: Phillips, Philip

Spin-momentum locking from topological quantum chemistry: Applications to multifold fermions

• DOI: 10.1103/physrevb.106.245101
• 发表时间: 2022-04
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Mao Lin;I. Robredo;N. B. M. Schröter;C. Felser;M. Vergniory;B. Bradlyn