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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.

该奖项支持固体中电子集体行为中量子力学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，通常情况下，电子流体的宏观性质（例如，导电性）可以相当经典地描述。例如，描述电子液体粘性流动的方程与描述水的方程非常相似，表现出本质上的经典行为。本项目超越了这一传统观点，发展了电子流的量子理论。首席研究员将专注于磁序与石墨烯三维类似物高能态的相互作用，称为Weyl和Dirac半金属。他将研究二维“拓扑绝缘体”边缘存在磁场时的电子运动，以及与粘性流体流动经典方程的偏差。这些主题将提出固体中的量子效应作为表征其微观性质的工具。这项研究将涉及研究生和本科生，并将促进他们在现代凝聚态理论方法方面的训练。教育方面的努力也将指向将现代课堂技术（例如“翻转”课堂）应用到个人项目的教学实践中。这个拓展项目的目的是培训高中生，让他们了解高等教育的要求和传统。本提案的目的是为电子自由度与宏观有序参数的相互作用以及（无序）无间隙拓扑相中相互作用的电子流体的输运和流体动力学性质提供理论见解，重点关注实验可观察到的现象。这项研究计划包括三个主要重点。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。推力是1。Weyl材料中磁自由度的异常感应电控制：PI将发展拓扑金属的电子自由度与宏观磁化之间相互作用的理论。具体来说，他将专注于i)异常诱导磁各向异性的异常检测和磁化控制，ii)电流诱导三维拓扑金属的自旋力矩理论，以及iii)带拓扑在织构磁相和磁激励中的表现。Weyl和其他几何金属中的非线性输运和磁输运现象：PI将研究三维和一维无间隙系统中根植于带几何（没有经典的“德鲁德”类似物）的非线性现象。具体方向将包括i)发展金属中e2b修正的一般理论，ii)无序Weyl半金属中的非线性异常霍尔效应，以及iii)一维拓扑和Rashba边缘上的动力学磁电效应和非线性输运理论。晶体中的异常流体力学：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将在此推力中研究的具体方向集中在i)流体力学体系中的异常输运，特别是在多谷贝里曲线（半）导体中，ii)无间隙系统中电子-电子碰撞产生的异常霍尔粘度，以及iii)晶体中的手性涡效应。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，特别注意具有非平凡拓扑的系统的现实方面。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。