Novel Phases of Electronic Insulators and Quantum Hall Systems

非技术概述该奖项支持对绝缘固体内大量相互作用电子的性质进行基础理论研究。这些电子的运动受量子力学原理的支配，并受到电子动能和电子间库仑斥力之间的竞争的影响。在过去的几年里，已经有可能在几种材料上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由两层晶格略有不同的单原子组成的材料层形成的二维云纹结构。人们已经在云纹物质中发现了令人着迷的现象，未来还会有其他重大发现。这项提议将开发理论工具来研究其中的一些现象和材料。这一理论将在云纹和其他材料中的新型电子绝缘体的许多正在进行的实验的背景下发展。目的是为了解和预测这些绝缘子的性能提供理论基础和工具。电子材料的基础研究为未来的电子技术进步提供了基础语料。它对具有多个自由度的系统的量子力学的关注，可能会在我们寻求对此类系统的控制和发展量子技术时，给我们很多有用的教训。教育部分涉及各级教育，包括凝聚态理论前沿领域的本科生。首席研究员将向这一研究领域以外的广大观众传达现代凝聚态物理的美丽。技术概述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。具体感兴趣的领域是描述在拓扑带中运动的强关联量子粒子。这个问题是某些莫尔石墨烯结构的核心，也是限制在单一朗道能级的量子霍尔系统的核心问题。重点将放在新理论概念和领域理论方法的一般发展上。如果可能，这些实验将被放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)从正在进行的莫尔石墨烯量子反常霍尔态实验中得到启发，解决部分填充拓扑带中强相关的基本问题，(2)继续发展PI的最低朗道能级理论，以解决包括费米子量子霍尔态在内的更广泛的问题。将采用广泛的分析和数值方法。首要目标是建立一个理论框架，描述部分填充的拓扑带中强相互作用的电子，这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方面的培训。PI将继续设计讲座，让研究生接触到实验方法和现代相关材料的现象学。讲座将向社会广泛提供。他还将继续与高能理论物理界合作，帮助凝聚态和高能物理的进步。这一奖项反映了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。

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.