CAREER: Topology and Geometry in Condensed Matter Systems

职业：凝聚态系统中的拓扑和几何

基本信息

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

项目摘要

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.

非技术摘要该职业奖支持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近期最具变革性的突破之一，它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。拓扑上非平凡的材料表现出金属表面状态，无论系统有多脏，这种状态都存在。然而，从实际角度来看，由于缺乏寻找现实拓扑系统的工具以及需要更好地理解拓扑响应，利用这些拓扑效应的设备的前景在很大程度上仍未实现。可以用来解决这些问题的一种工具是几何学。几何学进入了晶体对称性的描述（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开发对拓扑材料的新见解。 PI 将使用对称原理来确定通过拓扑材料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，目的是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。这项研究与本科生和研究生教育计划紧密结合，涉及 1) 开发关于电子结构中的贝里相和拓扑的高级研究生课程，目前课程中尚未详细介绍该课程，2)在暑期和学年期间指导本科生进行研究，以及 3) 使用统计物理学技术研究在线骚扰的推广计划，以展示物理学在数据科学中的应用。技术摘要该职业奖支持研究进入晶体几何和拓扑现象之间的相互作用，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，表明并非所有绝缘体都是平等的。拓扑材料最显着的实验特征是受保护的边缘态的存在，从而导致受保护的非耗散传导。然而，拓扑材料还具有显着的体积特性，例如非耗散传输系数、缺乏局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拓扑系统以前未研究的属性。这将通过研究 1 来实现。作为拓扑探针的响应：将研究霍尔粘度等几何传输系数，以阐明拓扑系统中各向异性、几何和流体动力学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拓扑结构和非线性电磁响应之间的联系。2．对称性在自由费米子能带拓扑中的作用：拓扑能带理论的数学基础将得到扩展，以便更好地理解晶体对称性在考虑拓扑非平凡能带中的作用。此外，对称原理将应用于不通约结构和准周期结构，以发展准周期系统中的拓扑相理论。 3．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多体拓扑相的研究中，并且将发展相关相中基本激发的能带表示理论。这个职业项目将有助于提供对量子物质的拓扑和强相关相有更丰富的理解。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。这项研究与本科生和研究生的教育计划紧密结合，涉及 1) 开发关于电子结构中的贝里相和拓扑的高级研究生课程，目前课程中尚未详细介绍该课程，2)指导本科生在暑期和学年进行研究，以及 3) 使用统计物理学技术研究在线骚扰的外展计划，以展示物理学在数据科学中的应用。该奖项反映了 NSF 的法定使命并且已经通过使用基金会的智力优点和更广泛的影响审查标准进行评估，认为值得支持。

项目成果

期刊论文数量（25）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Understanding the Use of Fauxtography on Social Media

了解仿照在社交媒体上的使用

DOI：
发表时间：
2021-06
期刊：
Proceedings of the International AAAI Conference on Weblogs and Social Media
影响因子：
0
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

Effective action approach to the filling anomaly in crystalline topological matter

晶体拓扑物质填充异常的有效作用方法

DOI：
10.1103/physrevb.107.195153
发表时间：
2023-02-22
期刊：
影响因子：
0
作者：
P. Rao;B. Bradlyn
通讯作者：
B. Bradlyn

Spin-resolved topology and partial axion angles in three-dimensional insulators

三维绝缘体中的自旋解析拓扑和部分轴子角

DOI：
10.1038/s41467-024-44762-w
发表时间：
2024-01-16
期刊：
Nature Communications
影响因子：
16.6
作者：
Lin, Kuan-Sen;Palumbo, Giandomenico;Guo, Zhaopeng;Hwang, Yoonseok;Blackburn, Jeremy;Shoemaker, Daniel P.;Mahmood, Fahad;Wang, Zhijun;Fiete, Gregory A.;Wieder, Benjamin J.;Bradlyn, Barry
通讯作者：
Bradlyn, Barry

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

倒谐波振荡器的物理学：从最低朗道能级到事件视界