CAREER: Correlations, responses and dynamics of interacting topological matter

该奖项部分由2021年美国救援计划法案（公法117-2）资助。该职业奖支持理论研究和教育，以研究材料中强相互作用电子的拓扑状态的新现象和动态特性。拓扑态是一类物质的相，它表现出对材料的任何局部变化都具有鲁棒性，例如产生空位（缺少原子）。拓扑绝缘体就是一个例子，它在整体上是绝缘的，但在其表面或边缘上保护导电电子。相比之下，一个普通的绝缘体在体积和表面或边缘都是绝缘的。某些拓扑态是特别有趣的，因为它们承载着可以应用于量子计算和信息技术的拓扑激发态。然而，这种拓扑状态可能只有在电子强烈相互作用时才会出现，并且很难实现。PI旨在从理论上预测和识别各种材料中这种强相互作用的拓扑状态。有前途的系统包括所谓的莫尔材料，它是通过以相对扭转角度堆叠二维原子薄材料而设计的，以及在强磁场中的二维金属。本研究的另一个重点是研究相互作用拓扑态中拓扑激发态的量子动力学演化，这对量子计算的应用至关重要。这些研究将采用解析和数值方法。所提出的研究将促进我们对拓扑材料的理解和技术应用。该奖项将包括对本科生和研究生的教育活动。PI将在普林斯顿理论科学中心的支持下组织研讨会和研讨会，为学生提供学习凝聚态物理前沿主题的机会。该奖项还将包括外展活动，包括建立一个团队网站，向非科学界传播团队的最新研究成果，举办公开讲座，以及创作艺术作品，将科学与更广泛的公众利益联系起来。该职业奖支持理论研究和教育，以研究相互作用拓扑状态的相关现象，拓扑响应和动力学，主要是在低维量子系统中，并探索它们在量子信息中的应用。PI将开发分析模型，微扰和非微扰方法，以及多体数值计算来进行研究。本研究将集中在四个方向上：(1)石墨烯和其他层状材料的堆叠和扭曲的二维波纹系统。PI将研究库仑和电子-声子相互作用下相关相和超导性的机制和拓扑结构，并预测它们的实验特征。一个重要的目标是寻找拓扑超导体。(2)分数量子霍尔系统中的竞争相。PI将从电子之间的实际库仑相互作用中研究复合费米子或玻色子之间的有效相互作用，以研究在GaAs和石墨烯中观察到的不同分数量子霍尔态的起源，以及在半奇整数朗道能级填充下的竞争基态。(3)二维拓扑物质的一般拓扑边缘态和体任意子相互作用的模式重构、量子相干性、混沌和动力学，以及相互作用对边缘态干涉仪的影响。这些研究将进一步应用于提出量子信息器件。(4)具有缺陷和无序的物质在三维拓扑相中的相互作用效应和响应，包括相互作用诱导的三维量子霍尔效应、轴子绝缘子和一般拓扑晶体态。该奖项将包括对本科生和研究生的教育活动。PI将在普林斯顿理论科学中心的支持下组织研讨会和研讨会，为学生提供学习凝聚态物理前沿主题的机会。该奖项还将包括外展活动，包括建立一个团队网站，向非科学界传播团队的最新研究成果，举办公开讲座，以及创作艺术作品，将科学与更广泛的公众利益联系起来。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。

This award is funded in part under the American Rescue Plan Act of 2021 (Public Law 117-2).NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to study novel phenomena and dynamical properties of topological states of strongly interacting electrons in materials. Topological states are a class of phases of matter which show properties that are robust against any local changes of the material, such as creating vacancies (missing atoms). An example is the topological insulator, which is insulating in the bulk, but has protected conducting electrons on its surface or edge. In contrast, a trivial insulator is insulating in both bulk and surface or edge. Certain topological states are particularly interesting as they host topological excited states which may be applied in quantum computation and information technologies. However, such topological states may only arise when electrons are strongly interacting and are difficult to realize.The PI aims at theoretically predicting and identifying such strongly interacting topological states in various materials. Promising systems include the so-called moiré materials which are engineered by stacking two-dimensional atomically thin materials at a relative twist angle, and two-dimensional metals in strong magnetic fields. The other focus of this research is to investigate the quantum dynamical evolutions of topological excited states in the interacting topological states, which are crucial for applications in quantum computation. Both analytical and numerical methods will be employed for these studies. The proposed research will advance our understanding and the technological applications of topological materials.This award will incorporate educational activities for undergraduate and graduate students. The PI will organize workshops and seminars with the support of the Princeton Center for Theoretical Science, providing the students opportunities to learn about topics at the forefront of condensed matter physics. The award will also contain outreach activities, including maintaining a group website to disseminate the team’s latest research to the non-scientific community, giving public lectures, and creating artworks bridging science and the broader interests of the general public.TECHNICAL SUMMARYThis CAREER award supports theoretical research and education to investigate the correlated phenomena, topological responses and dynamics of interacting topological states, dominantly in low-dimensional quantum systems, and to explore their applications in quantum information. The PI will develop analytical models, perturbative and nonperturbative methods, and many-body numerical computations to perform the research. This research will focus on four directions:(1) Two-dimensional moiré systems from stacking and twisting of graphene and other layered materials. The PI will investigate the mechanism and topology of the correlated phases and superconductivity under Coulomb and electron-phonon interactions, and predict their experimental signatures. An important goal is to search for topological superconductors.(2) Competing phases in fractional quantum Hall systems. The PI will study the effective interactions between composite fermions or bosons from realistic Coulomb interactions between electrons, to investigate the origin of different fractional quantum Hall states observed in GaAs and graphene, and the competing ground states at half-odd integer Landau level fillings.(3) The mode reconstruction, quantum coherence, chaos and dynamics of generic interacting topological edge states and bulk anyons of two-dimensional topological matter, and the effects of interaction on the edge state interferometers. These studies will be further applied to propose quantum information devices.(4) The interaction effects and responses in three-dimensional topological phases of matter with defects and disorder, including the interaction induced three-dimensional quantum Hall effect, axion insulators and generic topological crystalline states. This award will incorporate educational activities for undergraduate and graduate students. The PI will organize workshops and seminars with the support of the Princeton Center for Theoretical Science, providing the students opportunities to learn about topics at the forefront of condensed matter physics. The award will also contain outreach activities, including maintaining a group website to disseminate the team’s latest research to the non-scientific community, giving public lectures, and creating artworks bridging science and the broader interests of the general public.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.