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Quantum Mechanics of Interacting Electron Fluid in Berry-curved Materials

莓曲材料中相互作用电子流体的量子力学

基本信息

批准号：
2138008
负责人：
Dmytro Pesin
金额：
$ 37.5万
依托单位：
University of Virginia Main Campus
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-12-01 至 2024-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2138008&HistoricalAwards=false
关键词：
Quantum Mechanics Interacting Electron Fluid

项目摘要

Non-technical summaryThis award supports theoretical studies of experimentally measurable manifestations of quantum mechanics in the collective behavior of electrons in solids. Quantum mechanics has proven crucial to explaining the behavior of this electron fluid. However, more often than not, macroscopic properties (e.g., electrical conduction) of the electron fluid can be described quite classically. For instance, the equations describing viscous flow of the electronic liquid are very similar to those that describe water, showing essentially classical behavior. The present project goes beyond this traditional point of view in developing a quantum theory for electron flow.The Principal investigator will focus on the interaction of magnetic order with higher-energy states in three-dimensional analogs of graphene, called Weyl and Dirac semimetals. He will study electron motion in the presence of a magnetic field on the edge of a two-dimensional "topological insulator" and deviations from the classical equations for viscous fluid flow. These topics will bring out the quantum effects in solids as a characterization tool for their microscopic properties.The research will involve graduate and undergraduate students and will facilitate their training in modern methods of condensed-matter theory. The educational efforts will also be directed toward implementation of modern classroom techniques (e.g. the "flipped" classroom) into the teaching practices of the PI. The outreach program will be directed toward training high-school students and acquainting them with the demands and traditions of higher education.Technical summaryThe objective of this proposal is to provide theoretical insights into the interaction of electronic degrees of freedom with macroscopic order parameters as well as transport and hydrodynamic properties of the interacting electronic fluid in (disordered) gapless topological phases, with a strong focus on experimentally observable phenomena. The research program contains three main thrusts. The common thread connecting these thrusts is the quantum mechanics of electrons on the lattice, manifested through geometric phases. The thrusts are1. Anomaly-induced electric control of magnetic degrees of freedom in Weyl materials: the PI will develop the theory of interaction between the electronic degrees of freedom of a topological metal with a macroscopic magnetization. Specifically, he will focus on i) the anomaly-induced magnetic anisotropy for anomaly detection and magnetization control, ii) the theory of current-induced spin torques in 3D topological metals, and iii) the manifestations of band topology in textured magnetic phases and magnetic excitations.2. Nonlinear transport and magnetotransport phenomena in Weyl and other geometric metals: the PI will study nonlinear phenomena rooted in band geometry (not having classical "Drude" analogs) in 3D and 1D gapless systems. The specific directions will include i) developing a general theory of E2B-corrections to transport in metals, ii) non-linear anomalous Hall effect in disordered Weyl semimetals, and iii) the theory of kinetic magnetoelectric effect and nonlinear transport on 1D topological and Rashba edges.3. Anomalous hydrodynamics in crystals: the PI will develop the theory of quantum effects in electron-electron collisions and their influence on electronic hydrodynamics. The specific directions PI Pesin will pursue within this thrust focus on i) anomalous transport in the hydrodynamic regime, in particular in multi-valley Berry-curved (semi-)conductors, ii) the anomalous Hall viscosity from electron-electron collisions in gapless systems, and iii) chiral vortical effect in crystals.The methods of the project will include standard tools of many-body theory, including the Keldysh diagrammatic technique and the quantum kinetic equation approach to quantum transport, as well as some numerical modeling. The results of the program will be used to provide guidance for materials research, paying particular attention to the realistic aspects of systems with nontrivial topology.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.

非技术性总结该奖项支持量子力学在固体中电子集体行为的实验可测量表现的理论研究。量子力学已被证明对解释这种电子流体的行为至关重要。然而，通常，宏观性质（例如，电子流体的导电）可以相当经典地描述。例如，描述电子液体的粘性流动的方程与描述水的方程非常相似，基本上表现出经典行为。本项目超越了传统的观点，发展了电子流的量子理论。首席研究员将专注于三维石墨烯类似物（称为Weyl和Dirac半金属）中磁序与高能态的相互作用。他将研究在二维“拓扑绝缘体”边缘存在磁场的情况下的电子运动，以及粘性流体流动与经典方程的偏差。这些课题将把固体中的量子效应作为表征其微观性质的工具。研究将涉及研究生和本科生，并将促进他们在凝聚态理论的现代方法方面的培训。教育工作还将致力于将现代课堂技术（例如“翻转”课堂）应用于PI的教学实践。该推广计划将针对培训高中生，并使他们了解高等教育的要求和传统。技术概述本提案的目的是提供理论见解，了解电子自由度与宏观序参数的相互作用，以及相互作用电子流体的输运和流体动力学性质，（无序）无间隙拓扑相，重点放在实验观察到的现象。该研究计划包括三个主要方面。连接这些推力的共同线索是晶格上电子的量子力学，通过几何相位表现出来。推力为1. Weyl材料中磁自由度的异常诱导电控制：PI将发展拓扑金属的电子自由度与宏观磁化之间的相互作用理论。具体而言，他将专注于i）异常检测和磁化控制的异常诱导磁各向异性，ii）3D拓扑金属中电流诱导自旋力矩的理论，以及iii）织构磁相和磁激发中带拓扑的表现。Weyl和其他几何金属中的非线性输运和磁输运现象：PI将研究3D和1D无隙系统中的带几何（没有经典的“Drude”类似物）中的非线性现象。具体方向将包括i）发展E2 B-修正的一般理论，以输运在金属，ii）非线性异常霍尔效应在无序Weyl半金属，iii）理论的动力学磁电效应和非线性输运的一维拓扑和Rashba边缘.晶体中的反常流体力学：PI将发展电子-电子碰撞中的量子效应理论及其对电子流体力学的影响。PI Pesin将在这个推力范围内追求的具体方向集中在i）流体动力学机制中的异常输运，特别是在多谷Berry弯曲（半）导体中，ii）无间隙系统中电子-电子碰撞的异常霍尔粘度，以及iii）晶体中的手征涡旋效应。该项目的方法将包括多体理论的标准工具，包括Keldysh图解技术和量子输运的量子动力学方程方法，以及一些数值模拟。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。该奖项反映了NSF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。