Mesoscopic and many-body effects in topological phases of matter

该奖项支持材料中电子拓扑相的理论研究和教育。电子有一种叫做自旋的固有特性，它看起来就像一个小陀螺。电子的自旋也与其固有的磁性有关；它的行为就像一个小条形磁铁。当电子在材料中移动时，它将经历晶格中原子核心的磁场，这是相对论的结果。电子与磁场的相互作用产生自旋轨道相互作用。拓扑绝缘体是强自旋轨道相互作用的结果，这种相互作用导致材料在整体上是绝缘的，但具有覆盖表面和边缘的金属态，并且对缺陷和缺陷具有鲁棒性。PI将研究导电和电子动力学，包括当高磁场应用于拓扑绝缘体和Weyl半金属时，这是一种三维材料，具有类似于石墨烯原子薄片的电子状态。PI将研究与强自旋轨道相互作用有关的新现象。该研究的主要目的是为电子如何在拓扑相中运动，它们如何与原子晶格相互作用以及它们如何在拓扑相中与其他相互作用提供理论见解。主要关注Weyl半金属中的电子-原子晶格相互作用和集体模式，拓扑绝缘体无序表面上相互作用电子的输运，以及低维系统中的热力学和输运性质。该奖项还支持教育和外展活动。将特别注重确保妇女和少数民族享有平等的研究和教育机会，并鼓励来自代表性不足群体的学生参与研究。PI的目标是开发一个关于物理的学生奥林匹克项目。通过为研究生和本科生提供培训和监督，以及开发现代凝聚态物理的研究生课程序列，将进一步整合研究和教育活动。该奖项支持理论研究和教育，旨在了解物质拓扑相中的多体和介观现象。本研究的主要目的是考虑与拓扑绝缘体和Weyl半金属以及具有强自旋轨道耦合的Mott绝缘体相关的新现象，并推进具有非平凡拓扑的相的基本物理，超越理想晶格中的非相互作用电子。PI的主要研究方向是：1)集体模式及其在无间隙拓扑相中的相互作用：粒子的合作行为通常是电子相的定义性质。PI将考虑Weyl半金属中的电子-声子和电子-电子相互作用，并提取由此产生的集体模式提供的实验特征，以促进Weyl系统的实验发现。2)。无间隙系统中拓扑跃迁的特征，特别是在具有非平凡费米表面拓扑的系统中，磁击穿理论-在动量空间中强磁场中电子轨道之间的电子隧穿。这条研究路线将推动磁振荡现象成为一种能够发现各种能带结构拓扑跃迁的光谱工具。3)。拓扑表面的物理学：非线性输运，电子-电子相互作用和介观物理学。这个方向涉及考虑拓扑表面上二维电子气体特有的磁电、介观和非线性现象。4)。具有强自旋轨道相互作用的莫特绝缘子。这个PI将解决莫特金属-绝缘体跃迁的物理如何被强自旋轨道相互作用所改变的问题。本文认为基于拓扑莫特绝缘子的异质结构是一种实用的过渡金属氧化物异质结构模型体系。该项目的方法将包括多体理论的标准工具，包括Keldysh图解技术，以及量子输运的量子动力学方程方法。该计划的结果将用于为材料研究提供指导，特别注意具有非平凡拓扑的系统的现实方面。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on topological phases of electrons in materials. Electrons have an intrinsic property called spin where it appears as if the electron spins like a tiny top. The spin of the electron is also connected to its intrinsic magnetic properties; it behaves as though it was a tiny bar magnet. As an electron moves through a material it will experience a magnetic field from the atomic cores in the lattice as a consequence of the theory of relativity. The interaction of the electron with this magnetic field gives rise to the spin-orbit interaction.Topological insulators are a consequence of strong spin-orbit interaction which leads to material that is insulating in the bulk but has metallic states that cover the surface and edges and robust to defects and imperfections. The PI will investigate the conduction of electricity and the dynamics of electrons, including when a high magnetic field is applied to topological insulators and Weyl semimetals which are three dimensional materials that have electronic states analogous to those in atomically thin sheets of graphene. The PI will study new phenomena related to strong spin-orbit interaction. The main objective of the research is to provide theoretical insights into how electrons move through topological phases, how they interact with the atomic lattice and how they interact with other in topological phases. The main focus is on the electron-atomic lattice interaction and collective modes in Weyl semimetals, transport of interacting electrons on disordered surfaces of topological insulators, and thermodynamic and transport properties in low-dimensional systems. This award also supports education and outreach activities. A special focus will be given to ensuring that equal research and education opportunities exist for women and minorities, and encouraging students from underrepresented groups to participate in research. The PI aims to develop a student Olympiad program on physics. Further integration of research and educational activities will be reached through providing training and supervision to graduate and undergraduate students, and developing a graduate course sequence on modern condensed matter physics.TECHNICAL SUMMARYThis award supports theoretical research and education with the aim to understand many-body and mesoscopic phenomena in topological phases of matter. The primary objective of the study is to consider new phenomena related to topological insulators and Weyl semimetals, as well as Mott insulators with strong spin-orbit coupling and advance the basic physics of phases with nontrivial topology, beyond noninteracting electrons in ideal crystalline lattices. The PI aims to pursue research directions in the following areas: 1.) Collective modes and their interaction in gapless topological phases: Cooperative behavior of particles is often a defining property of an electronic phase. The PI will consider electron-phonon and electron-electron interactions in Weyl semimetals, and extract the experimental signatures provided by the resultant collective modes to facilitate the experimental discoveries of Weyl systems. 2.) Signatures of topological transitions in gapless systems, in particular, the theory of the magnetic breakdown - tunneling of electrons between electron orbits in momentum space in strong magnetic fields - in a system with non-trivial Fermi surface topology. This line of research will promote magneto-oscillation phenomena into a spectroscopic tool capable of discovering topological transitions in various band structures. 3.) Physics of topological surfaces: nonlinear transport, electron-electron interaction and mesoscopic physics. This direction involves considering magnetoelectric, mesoscopic and nonlinear phenomena unique to two-dimensional electron gases on topological surfaces. 4.) Mott insulators with strong spin-orbit interaction. This PI will address the question of how the physics of the Mott metal-insulator transition is modified by strong spin-orbit interaction. It will be argued that the heterostructures based on the Topological Mott insulators are useful model system for the realistic transition metal oxide heterostructures.The methods of the project will include standard tools of many-body theory, including the Keldysh diagrammatic technique, and quantum kinetic equation approach to quantum transport. The results of the program will be used to provide guidance for materials research, paying particular attention to realistic aspects of systems with nontrivial topology.