Novel phases of electronic insulators and quantum Hall systems

该奖项支持关于有趣的新型电子固体绝缘相的理论研究和教育。大多数固体的电子特性是在量子力学描述中理解的，量子力学描述了在构成固体的元素的带电原子核的背景中移动的大量相互作用的电子。在简单的固体中，物理学可以用一种近似的方法来理解，即把电子看作是相互独立运动的量子力学粒子。现代材料研究的一个主要主题是研究这种近似失效的材料，而不同电子的运动实际上是相关的。在这种材料中出现了令人着迷的现象；例子包括高温超导性，以及其他电子在固体内部分裂的新现象。最近一个重要的实验进展是在一个特别简单和可调的系统中，即在原子薄的石墨烯层中，观察到电子运动的这种强相关性。PI将开发新的概念和方法来处理不同背景下的这种电子系统。他将把从一个平台（如前面提到的石墨烯系统）中学到的经验应用到其他长期以来难以理解的已知平台上，反之亦然。从历史上看，这种对电子材料的基础研究产生了许多现代电子技术基础的概念。拟议的研究将有助于科学和技术知识的连续性，这将使未来的技术能够以基本的方式收获具有多个自由度的系统的量子力学行为。该研究项目将吸引研究生参与前沿研究，并在适当和可能的情况下，吸引本科生参与。该奖项支持研究某些云纹石墨烯结构中相关电子绝缘体的研究和教育，与量子霍尔系统的共性，以及无序受挫量子磁体。重点将放在新的理论概念和实地理论方法的总体发展上。在可能的情况下，这些将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。这方面的建议项目包括：i)通过分析和数值方法的结合，研究abc - stacking三层石墨烯及相关系统中云纹超晶格的微观模型；ii)一个特定非阿贝尔量子霍尔态的微观最低朗道能级理论，寻求建立一个捕捉拓扑和非普适性质的解析理论；iii)二维受挫量子磁体中无序效应的几个一般问题。该项目将提供关键的见解和方法，这将有助于解释云纹石墨烯系统、量子磁体和玻色子量子霍尔态可能的未来冷原子实现的实验结果。PI将继续努力设计讲座，让研究生接触实验方法和现代相关材料的现象学。在可能的情况下，本科生将参与研究。他还将继续参与高能社区，以帮助凝聚态物质和高能物理的进步。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 on interesting new kinds of insulating phases of electronic solids. The electronic properties of most solids are understood within a quantum mechanical description that accounts for a large number of interacting electrons moving in the background of the charged atomic cores of the elements that comprise the solid. In simple solids the physics can be understood within an approximation that treats the electrons as quantum mechanical particles that move independently of one another. A major theme of modern materials research is on materials in which this approximation fails and the motion of different electrons is in fact correlated. Fascinating phenomena emerge in such materials; examples include high-temperature superconductivity, and other novel phenomena where the electrons appear to break apart inside the solid. An important recent experimental advance is the observation of such strong correlation of electronic motion in a particularly simple and tunable system, namely in atomically thin layers of graphene. The PI will develop new concepts and methods to deal with such electronic systems in diverse contexts. He will apply the lessons learnt from one platform, such as the graphene system mentioned before, to other known platforms that have long resisted understanding, and vice versa.Historically, such fundamental research on electronic materials has generated many of the concepts that underlie modern electronic technology. The proposed research will contribute to the continuum of scientific and technological knowledge that will enable future technology that harvests the quantum mechanical behaviors of systems with many degrees of freedom in fundamental ways. The research project will engage graduate students in cutting-edge research, and when appropriate and possible, undergraduates. TECHNICAL SUMMARYThis award supports research and education on studying correlated electronic insulators in certain moire graphene structures, commonalities with quantum Hall systems, and of disordered frustrated quantum magnets. 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 of numerical work on specific microscopic models. The proposed projects in this broad area include: i) a study of microscopic models for the Moire superlattice in ABC-stacked trilayer graphene and related systems through a combination of analytical and numerical methods, ii) a microscopic Lowest Landau Level theory of a particular non-abelian quantum Hall state, seeking to establish analytically a theory that captures both topological and non-universal properties, iii) several general questions on disorder effects in 2D frustrated quantum magnets. The project will provide key insights and methods that will be useful in interpreting the results from experiments on Moire graphene systems, quantum magnets, and possible future cold-atom realizations of bosonic quantum Hall states.The PI will continue his efforts to design lectures to expose graduate students to experimental methods and the phenomenology of modern correlated materials. Undergraduates will be involved in the research when possible. He will also continue his engagement with the high-energy 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.