Correlated Electron Physics in Graphene and Other Novel Quantum Materials

非技术性总结该奖项支持理论研究和教育，以进一步了解量子力学如何在原子水平上确定大量相互作用粒子的物质状态。这种动力学的舞台是真实的量子材料，在世界各地的实验室中使用现代实验工具进行设计和研究。最终的实际目标是利用所获得的理解来设计具有所需性能的新材料和结构。超导性的发现-没有任何阻力的电流流动-在由两片石墨烯组成的物理系统中，每一个碳原子都很薄，并且精确地堆叠在彼此之上，已经开始了与上述目标相一致的新的前沿研究领域。此外，许多这样的材料结合了联合收割机的拓扑学的现代概念与固态物理学的基本概念，描述了强相互作用的电子系统的行为，这是一个知识前沿仍然在很大程度上未被探索。PI将使用一系列现代分析和数值工具来研究此类系统。该项目将涉及一名研究生，该研究生将通过沉浸在凝聚态物理前沿开放问题的协作环境中，接受分析和计算方法以及科学交流方面的培训。它还将允许学生前往并参加会议和学校，从而与更广泛的科学界接触。将开发的技能是在STEM领域的许多成功的职业生涯必不可少的。技术总结该奖项支持基础研究和教育，旨在了解相关电子在新型量子材料的属性。长期目标是利用这种理解来设计具有所需功能的新材料和结构，以及推进预测分析所需的理论工具。PI的研究和教育活动集中在莫尔材料的理论描述上，包括扭曲的双层石墨烯。这样的系统结合了联合收割机拓扑非平凡的能带结构和强电子关联的现代概念。从广义上讲，该项目的主要目的是了解负责的基本机制-和性质-在窄带的相称填充处观察到的相关绝缘体相，以及在各种莫尔结构中的一般不相称填充处观察到的附近超导性。PI将使用一系列分析和数值工具来研究这个问题，包括强耦合展开、变分平均场理论和密度矩阵重整化群。该项目的一个重要组成部分是同时开发简化模型，捕捉在更多的数字技术中获得的发现的物理本质。这些模型将使人们对现有材料中的物理现象有更深入的理解，也将为进一步的定性预测提供更大的灵活性，而这些预测在数值上是不容易实现的。这些项目将涉及一名研究生，他将通过沉浸在一个合作环境中，致力于解决凝聚态物理学前沿的开放问题，接受分析和计算方法以及科学交流方面的培训。它还将允许学生前往并参加会议和学校，从而与更广泛的科学界接触。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

NONTECHNICAL SUMMARYThis award supports theoretical research and education to further our understanding of how quantum mechanics determines the state of matter of a large collection of interacting particles at the atomic level. The stages on which such dynamics plays out are real quantum materials, designed and studied within laboratories around the world using modern experimental tools. The ultimate practical goal is to use the gained understanding for designing new materials and structures with desired properties.The discovery of superconductivity --flow of electrical current without any resistance-- in a physical system composed of two sheets of graphene, each one carbon atom thin and precisely stacked on top of each other, has started a new frontier research field aligned with the above goals. In addition, many such materials combine modern notions of topology with basic concepts of solid-state physics describing the behavior of strongly interacting electron systems, an intellectual frontier still largely unexplored. The PI will study such systems using an arsenal of modern analytical and numerical tools.The projects will involve a graduate student, who will be trained in analytical and computational methods, as well as in scientific communication, via immersion in a collaborative environment working on open problems at the frontier of condensed matter physics. It will also allow the student to travel to and participate in conferences and schools, and thus engage with the broader scientific community. The skills that will be developed are essential for many successful careers in STEM fields.TECHNICAL SUMMARYThis award supports fundamental research and education aimed at understanding properties of correlated electrons in novel quantum materials. The long-term goal is to use such understanding to design new materials and structures with desired functionalities, as well as to advance theoretical tools needed for predictive analysis. The PI's research and educational activity is centered on the theoretical description of moire materials, including twisted bilayer graphene. Such systems combine modern notions of topologically nontrivial band structure and strong electron correlations. Broadly, the main thrust of the project is to understand the underlying mechanism responsible for -- and the nature of -- the correlated insulator phases observed at commensurate fillings of the narrow bands, and the nearby superconductivity observed at generally incommensurate fillings in various moire structures. The PI will study the problem using an arsenal of analytical and numerical tools, including strong-coupling expansions, variational mean-field theory, and density-matrix renormalization group. An important part of the project is the simultaneous development of simplified models capturing the physical essence of the findings obtained within more numerically involved techniques. Such models will engender deeper understanding of the physics playing out in existing materials, and will also allow greater flexibility in further qualitative predictions not easily achieved numerically.The projects will involve a graduate student, who will be trained in analytical and computational methods, as well as in scientific communication, via immersion in a collaborative environment working on open problems at the frontier of condensed matter physics. It will also allow the student to travel to and participate in conferences and schools, and thus engage with the broader scientific community. The skills that will be developed are essential for many successful careers in STEM fields.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.