Topological Phases and Correlation Phenomena in Complex Materials

该奖项支持关于新型固体材料及其电子之间的排斥所产生的惊人现象的理论研究和教育。理想的自由电子与固体的正电核相互作用，但彼此之间不相互作用，已经可以产生惊人的效果：金属、电绝缘体和半导体之间的差异已经可以在这个自由电子的水平上被理解。提出的工作的一部分是关于新发现的材料的拓扑状态，可以使用被称为拓扑的数学分支来分析。一些拓扑相可以用自由电子来理解，而另一些则需要电子之间的强相互作用。PI将研究这两种拓扑相。两者都可以在大块绝缘体表面支持原子薄的导电层，这具有技术应用的潜力。PI将追求一个主要的新研究方向，以了解金属的拓扑效应和光反射和传输等光学特性，以最近在绝缘体和传输特性（如电导率）方面的成功为基础。电子之间的相互作用对于使系统达到热平衡的稳定状态，或者换句话说，具有明确定义的温度是至关重要的。研究的第二个重点是了解远离稳定平衡状态的量子物质，比如某些半导体器件。有迹象表明，当量子效应特别强时，会出现许多新的状态和现象。该奖项还支持具有共同目标的更广泛影响。该项目将有助于培养凝聚态物理重要领域的研究生，其中一些有可能产生实用技术。PI将继续指导本科生、研究生和博士后，特别关注目前在物理科学领域代表性不足的群体成员，包括担任加州大学伯克利分校新项目的物理教师顾问。一本通俗易懂的关于物质拓扑相的书，包括量子霍尔效应、自旋液体和拓扑绝缘体，将与一位国际合作者共同撰写。偶尔对普通大众和K-12课程的讲座将有助于传播对物理和材料科学的热情。PI将继续在伯克利组织会议和专题研讨会，以宣传研究进展，并将寻求通过其他形式的服务为凝聚态物质社区做出贡献。该奖项支持关于量子系统中相互作用所产生的新秩序的理论研究和教育。强相互作用的量子系统可以表现出新的秩序，并表现出许多不同的时间演化。这项研究在理解上有三个重点：在无间隙系统（金属）中，从自由电子带金属到在高磁场中产生的强相关态，作为拓扑相基础的相同几何性质如何具有可观察到的结果。结合数值矩阵积态方法和解析理论研究平移不变系统和无序系统的一维量子动力学。两个主要目标是理解强相关、平移不变、不可积模型中的异常输运，并发展多体定位、纠缠和量子混沌之间的联系。3. 分数粒子如马约拉纳费米子如何改变拓扑相中的非平衡动力学。这些项目的研究涉及到先进的分析和数值方法的结合，并将影响凝聚态物理的许多领域，包括实验。该奖项还支持具有共同目标的更广泛影响。该项目将有助于培养凝聚态物理重要领域的研究生，其中一些有可能产生实用技术。PI将继续指导本科生、研究生和博士后，特别关注目前在物理科学领域代表性不足的群体成员，包括担任加州大学伯克利分校新项目的物理教师顾问。一本通俗易懂的关于物质拓扑相的书，包括量子霍尔效应、自旋液体和拓扑绝缘体，将与一位国际合作者共同撰写。偶尔对普通大众和K-12课程的讲座将有助于传播对物理和材料科学的热情。PI将继续在伯克利组织会议和专题研讨会，以宣传研究进展，并将寻求通过其他形式的服务为凝聚态物质社区做出贡献。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on new kinds of solid materials and the surprising phenomena that emerge from the repulsion between their electrons. Idealized free electrons that interact with the positive nuclei of the solid but not with each other can already give surprising effects: the differences between metals, electrical insulators, and semiconductors can already be understood at this free-electron level. One part of the proposed work is concerned with newly discovered materials in topological states that can be analyzed using the branch of mathematics known as topology. Some topological phases can be understood in terms of free electrons, while others require strong interactions between the electrons. The PI will investigate both kinds of topological phases. Both can support atomically thin conducting layers at the surface of a bulk insulator, which have potential for technological applications. The PI will pursue a major new research direction to understand topological effects in metals and in optical properties such as light reflection and transmission, building on recent success in insulators and for transport properties such as conductivity.Interactions between the electrons are crucial in allowing systems to reach the steady state of thermal equilibrium, or put another way, to have a well-defined temperature. The second focus of the research is to understand quantum matter far from the steady state of equilibrium, like certain semiconductor devices. There are indications that numerous new states and phenomena emerge when quantum effects are particularly strong.This award also supports broader impacts with a common goal. This project will contribute to the training of graduate students in important fields of condensed matter physics, some of which have the potential to yield practical technologies. The PI will continue mentoring at the undergraduate, graduate, and postdoctoral levels with special attention to members of groups currently underrepresented in the physical sciences, including service as physics faculty advisor to a new UC Berkeley program. An accessible book on topological phases of matter, including the quantum Hall effect, spin liquids, and topological insulators, will be co-authored with an international collaborator. Occasional lectures to the lay public and K-12 classes will help spread enthusiasm for physics and materials science. The PI will continue to organize conferences and a focused seminar at Berkeley in order to propagate research developments, and will also seek to contribute to the condensed matter community through other forms of service.TECHNICAL SUMMARYThis award supports theoretical research and education on new kinds of order that emerge has a consequence of interactions in quantum systems. Strongly interacting quantum systems can exhibit new kinds of order and show many different kinds of temporal evolution. The research has three thrusts on understanding: 1. how the same geometric properties that underlie topological phases in gapped systems have observable consequences in gapless systems (metals) ranging from free-electron band metals to strongly correlated states arising in high magnetic fields.2. quantum dynamics in one dimension in both translation-invariant systems and disordered systems through a combination of numerical matrix-product-state methods and analytic theory. The two main goals are to understand anomalous transport in strongly correlated, translation-invariant, non-integrable models and to develop connections between many-body localization, entanglement, and quantum chaos. 3. how fractional particles such as Majorana fermions modify non-equilibrium dynamics in topological phases.Research on these projects involves a combination of advanced analytical and numerical methods and will impact many areas of condensed matter physics, including experiments.This award also supports broader impacts with a common goal. This project will contribute to the training of graduate students in important fields of condensed matter physics, some of which have the potential to yield practical technologies. The PI will continue mentoring at the undergraduate, graduate, and postdoctoral levels with special attention to members of groups currently underrepresented in the physical sciences, including service as physics faculty advisor to a new UC Berkeley program. An accessible book on topological phases of matter, including the quantum Hall effect, spin liquids, and topological insulators, will be co-authored with an international collaborator. Occasional lectures to the lay public and K-12 classes will help spread enthusiasm for physics and materials science. The PI will continue to organize conferences and a focused seminar at Berkeley in order to propagate research developments, and will also seek to contribute to the condensed matter community through other forms of service.