Novel Phases of Electronic Insulators and Quantum Hall Systems

该奖项支持对绝缘固体中大量相互作用电子特性的基础理论研究。这些电子的运动受量子力学原理支配，并受到电子动能和电子间库仑斥力之间竞争的影响。在过去的几年里，已经有可能在几种材料中通过实验来调整这些不同的竞争效应。其中最引人注目的是二维云纹结构，它是由两个晶格略有不同的单原子厚材料层聚集而成的。在云纹材料中已经发现了令人着迷的现象，未来还会有其他深刻的发现。本提案将发展理论工具来研究这些现象和材料。该理论将在许多正在进行的关于云纹和其他材料的新型电子绝缘体的实验中得到发展。目的是为理解和预测这些绝缘体的性质提供理论基础和工具。电子材料的基础研究为未来电子技术的进步提供了基础语料库。它对具有多个自由度的系统的量子力学的关注，将潜在地教给我们许多有用的经验教训，因为我们试图控制这样的系统并开发量子技术。教育部分涉及各级教育，包括凝聚态理论前沿的本科生。首席研究员将向本研究领域之外的广大受众传达现代凝聚态物理之美。该奖项支持理论和计算研究，以及有关电子绝缘体和相关量子霍尔系统中发生的新现象的相关教育。具体的兴趣领域是描述在拓扑带中移动的强相关量子粒子。这个问题是某些云纹石墨烯结构的核心问题，也是限于单一朗道能级的量子霍尔系统的核心问题。重点将放在新的理论概念和领域理论方法的总体发展上。在可能的情况下，这些将被放置在特定材料的实验或特定微观模型的数值工作的背景下。研究将(1)解决部分填充拓扑带中强相关的基本问题，这些问题受到正在进行的云纹石墨烯量子反常霍尔态实验的启发，(2)继续PI最低朗道能级理论的发展，以解决更广泛的问题，包括费米子量子霍尔态。广泛的分析和数值方法将被采用。总体目标是建立一个理论框架来描述部分填充的拓扑带中的强相互作用电子，可以解决物理学的普遍和非普遍方面。在这项研究中，研究生和本科生将接受现代凝聚态物理的培训。PI将继续设计讲座，让研究生接触实验方法和现代相关材料的现象学。讲座将广泛提供给社会各界。他还将继续参与高能理论物理社区，以帮助凝聚态物质和高能物理的发展。该奖项反映了美国国家科学基金会的法定使命，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。

Nontechnical SummaryThis award supports foundational theoretical research on the properties of a large collection of interacting electrons inside an insulating solid. The motion of these electrons is governed by the principles of quantum mechanics and is affected by the competition between the electron’s kinetic energy, and the inter-electron Coulomb repulsion. In the last few years, it has become possible to tune these different competing effects experimentally in several materials. Most striking amongst these are two-dimensional moire structures formed by bringing together two single-atom thick layers of materials whose lattices are slightly different. Fascinating phenomena have already been found in moire materials, and there is great promise for other profound future discoveries. This proposal will develop theoretical tools to study some of these phenomena and materials. The theory will be developed in the context of the many ongoing experiments on novel electronic insulators in moire, and other, materials. The goal is to provide a theoretical foundation and the tools needed to understand and predict the properties of these insulators. Fundamental research on electronic materials provides the foundational corpus upon which future electronic technological progress can build. Its focus on the quantum mechanics of systems with many degrees of freedom will potentially teach us many useful lessons as we seek to gain control over such systems and develop quantum technologies. The education component involves education at all levels, including undergraduate students at the frontiers of condensed matter theory. The Principal Investigator will convey the beauty of modern condensed matter physics to a broad audience outside this research field. Technical SummaryThis award supports theoretical and computational research, and associated education on the novel phenomena that happen in electronic insulators, and related quantum Hall systems. Specific areas of interest are the description of strongly correlated quantum particles that move in a topological band. This problem is central to certain moire graphene structures, and to quantum hall systems restricted to a single Landau level. The emphasis will be on general development of new theoretical concepts and field theoretic methods. When possible, these will be placed in the context of either experiments on specific materials or numerical work on specific microscopic models. Research will (1) address basic questions on strong correlation in a partially filled topological band inspired by ongoing experiments on quantum anomalous Hall states in moire graphene, and (2) continue the PI's development of a lowest Landau level theory to solve a wider range of problems, including fermionic quantum Hall states. A broad range of analytical and numerical methods will be employed. The overarching goal is to develop a theoretical framework to describe strongly interacting electrons in a partially filled topological band that can address both universal and non-universal aspects of the physics. Graduate and undergraduate students will be trained in modern condensed matter physics during this research. The PI will continue to design lectures to expose graduate students to experimental methods and the phenomenology of modern correlated materials. Lectures will be made widely available to the community. He will also continue his engagement with the high energy theoretical physics community to aid advances in both condensed matter and high energy physics.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.