Strong Electron Correlations and Quantum Critical Phenomena

该奖项支持凝聚态物理的理论研究和教育，重点关注强相关电子现象的各个方面。这个项目的核心思想有三个：1) Mott间隙的谱权转移表明掺杂Mott绝缘体的正确低能理论涉及电荷2e玻色子场；2)低于临界直径的纳米线中约瑟夫森效应的抑制源于超导态的开始，其配对对称性与引线中的s波态正交；3)金属薄膜合金中金属态的起源是由玻璃性驱动的，它们显示出假定的绝缘体-超导体转变。这个项目的目标是确认和阐明这些想法。该项目侧重于开发理论工具和新思路，以阐明由大库仑排斥或量子临界点附近系统主导的关键实验系统。当然，在无序存在的情况下，新的相是可能的，比如玻璃。玻色子或费米子的金属相究竟是如何在二维空间中获得的还不得而知。这个项目继续发展这个问题的一个可能的解决方案，以及一个系统的方法来接近强相关问题的许多方面。更广泛的影响：该奖项支持寻求理论固体物理博士学位的研究生。由于大库仑排斥力和无序问题是固态物理的核心，学生在这方面获得专业知识是必不可少的。除了培养研究生外，还将实现其他几个广泛的教育目标。首先，由于PI致力于向下一代学生传播理论固体物理学的现状，他编写了一本急需的研究生教科书“高级固体物理学”。PI计划一个新的版本，将纳入新的材料强相关系统，这有助于整合前沿研究到教育文本。伊利诺斯大学开设了一门名为“量子相变”的新课程，这是美国国家科学基金会资助的研究的直接成果。该项目的第二个重要特征是PI作为伊利诺伊州物理系和工程学院（COE）少数族裔学生的高度可见和有效的榜样的影响。该项目的一个新颖的外联组成部分是PI参与协助发展中国家的科学家。他最近在特立尼达和多巴哥组织了一次关于“混沌和量子临界性”的国际研讨会，帮助加勒比地区的科学家了解强相关电子材料的前沿问题。此外，PI还是Bardeen-Cooper-Schrieffer超导理论出版50周年研讨会、教育和博物馆推广活动的组织委员会主席。非技术总结：该奖项支持凝聚态物理的理论研究和教育。该提案的重点是发现和理解当电子之间的相互作用非常大并导致其运动中的强相关性时发生的物质的新状态。高温超导体是一类电子之间的强相互作用导致物质新状态的材料的例子。在PI将研究的物质状态中，有由于电子之间的强相互作用而产生的绝缘状态，称为莫特绝缘体，以及在薄膜中观察到的超导和绝缘状态之间发生的转换中可能隐藏的新物质状态。PI将专注于发展理论工具和新思想，以阐明关键实验系统的潜在物理学，并了解新的金属态是如何产生的。PI是伊利诺伊州物理系和工程学院（COE）少数族裔学生的一个非常明显和有效的榜样。该奖项支持他的一些教育和推广活动，包括研究生水平的理论凝聚态物理教育，重点关注该领域的核心问题。PI的研究将有助于他的工作，以创建他的研究生水平的教科书，“先进的固体物理”的新版本，这将纳入新的材料，并将前沿研究整合到文本。PI协助发展中国家科学家使其研究现代化的活动是这个项目的外联部分。他作为研讨会和Bardeen-Cooper-Schrieffer超导理论出版50周年的教育和博物馆推广活动的组织委员会主席的活动是他推广工作的另一个组成部分。

This award supports theoretical research and education in condensed matter physics with a focus on aspects of strongly correlated electron phenomena. Three key ideas lie at the heart of this project: 1) spectral weight transfer across the Mott gap suggests that the correct low-energy theory of doped Mott insulators involves a charge 2e bosonic field, 2) the suppression of the Josephson effect in nanowires below a critical diameter originates from the onset of a superconducting state with a pairing symmetry that is orthogonal to the s-wave state in the leads, and 3) the origin of the metallic state in thin metal film alloys displaying a putative insulator-superconductor transition is driven by glassiness. The goal of this project is to confirm and elucidate each of these ideas. This project focuses on developing theoretical tools and new ideas to elucidate key experimental systems that are dominated by large Coulomb repulsions or systems near quantum critical points. Of course in the presence of disorder, new phases are possible, such as glasses. Precisely how metallic phases obtain in two dimensions for either bosons or fermions is not known. This project continues to develop a possible resolution of this problem, as well as a systematic way of approaching many aspects of the strongly correlated problem. Broader Impact: This award supports graduate students seeking their PhD degrees in theoretical solid state physics. As the large Coulomb repulsion and disorder problems are central to solid state physics, it is essential that students gain expertise in this area. In addition to the training of graduate students, several other broad educational goals will be met. First, as a result of the PI's commitment to the communication of the current status of theoretical solid state physics to the next generation of students, he has written a much-needed graduate textbook, "Advanced Solid State Physics." The PI plans a new edition will which will incorporate new material on strongly correlated systems which helps integrate forefront research into an educational text. A new course at Illinois, entitled "Quantum Phase Transitions," has been developed as a direct outgrowth from NSF-funded research. A second important feature of this project is the PI's impact as a highly visible and effective role model for minority students in the Department of Physics and the College of Engineering (COE) at Illinois. A novel outreach component of the project is the PI's involvement in assisting scientists in developing countries. He recently organized an international workshop in Trinidad and Tobago on "Mottness and Quantum Criticality" which helped to introduce scientists from the Caribbean to frontier problems in strongly correlated electron materials. In addition, the PI is the Chair of the organizing committee for the symposium and educational and museum outreach for the 50th anniversary of the publication of the Bardeen-Cooper-Schrieffer theory of superconductivity. NON-TECHNICAL SUMMARY:This award supports theoretical research and education in condensed matter physics. The proposal focuses on the discovery and understanding of new states of matter that occur when the interactions among electrons are very large and lead to strong correlations in their motion. High temperature superconductors are examples of a class of materials in which strong interactions among electrons lead to new states of matter. Among the states of matter that the PI will study are the insulating state that arises as a consequence of strong interactions among electrons, known as a Mott insulator, and new states of matter that may be hidden in a transformation that takes place between superconducting and insulating states observed in thin films. The PI will focus on developing theoretical tools and new ideas to elucidate the underlying physics of key experimental systems and to understand how new metallic states arise.The PI is a highly visible and effective role model for minority students in the Department of Physics and the College of Engineering (COE) at Illinois. This award supports some of his education and outreach activities, including graduate level education in theoretical condensed matter physics with a focus on central problems of the field. The PI's research will contribute to his work to create a new edition of his graduate level textbook, "Advanced Solid State Physics," which will incorporate new material and integrate forefront research into the text. The PI activities in assisting scientists in developing countries to modernize their research constitute an outreach component of this project. His activities as Chair of the organizing committee for the symposium and educational and museum outreach for the 50th anniversary of the publication of the Bardeen-Cooper-Schrieffer theory of superconductivity are another component of his outreach efforts.