Mesoscopic and many-body effects in topological phases of matter

非技术性总结该奖项支持材料中电子拓扑相的理论研究和教育。电子有一个内在的属性，称为自旋，它看起来就像电子像一个小陀螺一样旋转。电子的自旋也与其固有的磁性有关;它的行为就像一个微小的条形磁铁。根据相对论，当电子穿过材料时，它将经历来自晶格中原子核的磁场。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本体中是绝缘的，但具有覆盖表面和边缘的金属态，并且对缺陷和瑕疵具有鲁棒性。PI将研究电的传导和电子的动力学，包括当高磁场施加到拓扑绝缘体和Weyl半金属时，这些材料是三维材料，其电子状态类似于石墨烯的原子薄片。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提供理论见解，了解电子如何通过拓扑相移动，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。主要的重点是电子-原子晶格相互作用和集体模式外尔半金属，相互作用的电子在拓扑绝缘体的无序表面上的输运，以及低维系统的热力学和输运性质。该奖项还支持教育和外联活动。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，并鼓励代表性不足群体的学生参加研究。PI的目标是开发一个关于物理的学生奥林匹克计划。通过对研究生和本科生的培训和指导，以及开发现代凝聚态物理学的研究生课程序列，将进一步实现研究和教育活动的整合。技术概述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。这项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结构的相的基本物理，超越理想晶格中的非相互作用电子。PI的目的是追求在以下领域的研究方向：1。无隙拓扑相中的集体模及其相互作用：粒子的合作行为通常是电子相的定义性质。PI将考虑外尔半金属中的电子-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签名，以促进外尔系统的实验发现。 2.）无间隙系统中拓扑转变的特征，特别是磁击穿理论-在具有非平凡费米表面拓扑的系统中，在强磁场中动量空间中电子轨道之间的电子隧穿。这条研究线将促进磁振荡现象成为一种光谱工具，能够发现各种能带结构中的拓扑跃迁。 3.）第三章拓扑表面物理：非线性输运、电子-电子相互作用与介观物理。这个方向涉及到考虑磁电，介观和非线性现象独特的二维电子气的拓扑表面。 4.）具有强自旋轨道相互作用的莫特绝缘体。这个PI将解决莫特金属-绝缘体转变的物理如何被强自旋-轨道相互作用修改的问题。基于拓扑Mott绝缘体的异质结构是一个很好的过渡金属氧化物异质结构的模型系统，该项目的研究方法包括多体理论的标准工具，包括Keldysh图解法和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，特别关注具有非平凡拓扑结构的系统的现实方面。

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.