Correlated Electron Physics in Graphene and Other Novel Quantum Materials

该奖项支持理论研究和教育，以进一步了解量子力学如何决定原子水平上大量相互作用粒子的物质状态。这种动力学的舞台是真正的量子材料，在世界各地的实验室使用现代实验工具设计和研究。最终的实际目标是利用获得的理解来设计具有所需性能的新材料和结构。在由两层石墨烯组成的物理系统中发现超导——电流无任何阻力流动，每层石墨烯都是一个碳原子薄，彼此精确堆叠在一起，开启了一个与上述目标一致的新前沿研究领域。此外，许多这样的材料结合了现代拓扑概念和描述强相互作用电子系统行为的固态物理学的基本概念，这是一个很大程度上尚未探索的知识前沿。PI将使用一系列现代分析和数值工具来研究这些系统。这些项目将涉及一名研究生，他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。要发展的技能对于许多STEM领域的成功职业至关重要。该奖项支持旨在理解新型量子材料中相关电子特性的基础研究和教育。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云纹材料的理论描述上，包括扭曲的双层石墨烯。这样的系统结合了拓扑非平凡带结构和强电子相关性的现代概念。总的来说，该项目的主要目的是了解在窄带的相应填充处观察到的相关绝缘体相的潜在机制和性质，以及在各种云纹结构中通常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。该项目的一个重要部分是同时开发简化模型，以捕获在更多涉及数值的技术中获得的发现的物理本质。这样的模型将使人们对现有材料中的物理现象有更深的理解，也将使进一步的定性预测具有更大的灵活性，而这些预测在数字上是不容易实现的。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。要发展的技能对于许多STEM领域的成功职业至关重要。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 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.