Theory and Application of Berry Phase Methods in Solids

固体浆果相法的理论与应用

• 批准号: 1408838
• 负责人: David Vanderbilt
• 金额: $ 56万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2019-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1408838&HistoricalAwards=false
• 关键词: Theory; Application; Berry; Phase; Methods

NON-TECHNICAL SUMMARYIn the last two decades, there has been a growing appreciation that certain mathematical concepts from differential geometry and topology are sometimes central to the understanding of the behavior of electrons in crystalline solids. The electrons are described by quantum-mechanical wavefunctions, and the manner in which these vary with momentum encodes many kinds of information about the solid, especially its electrical and magnetic responses and their coupling with each other. When the wavefunctions become twisted in momentum space, this results in so-called "topological insulator" states, which have been the focus of intense research interest in the last decade. By definition, electric currents cannot flow in the interior of an insulator, but a topological insulator has the unusual property that there are guaranteed to be current-carrying channels at the surfaces. The present research program is designed to further develop the formal theory of such effects, to invent robust and efficient computational algorithms for computing the related properties of solids, and to carry out a computational search for materials displaying new or enhanced properties. The project will lead to the development of algorithms that will ultimately be implemented in open-source code packages and made available to the wider electronic-structure community. It will also contribute to the development of novel materials that are promising for commercial applications, especially ones involving the coupling of electrical and magnetic responses. Training and mentorship of junior researchers (graduate students and postdocs) will take place, contributing to scientific workforce development.TECHNICAL SUMMARYThis research program is focused on the electronic properties of topological insulators or other materials in which orbital currents play an important role. The objectives are (i) to further develop the formal theory of such systems, making use of the mathematical concepts of Berry phase, Berry curvature, and Chern number from differential geometry; (ii) to invent accurate and efficient computational methods for computing materials properties related to these mathematical concepts; and (iii) to use computational methods to identify promising new materials or structures in which these properties can manifest themselves, potentially leading to technological applications. While much recent work has concentrated on time-reversal invariant topological insulators such as Bi2Se3, the emphasis here will be on quantum anomalous Hall or Chern insulators, axion insulators, and Weyl semimetals, in which time-reversal symmetry is spontaneously broken. While the possibility of the Chern-insulator state was pointed out already 25 years ago, it has only recently been demonstrated experimentally, and that only at low temperature. Strategies will be developed for theoretically identifying possible two-dimensional Chern-insulator states accessible to experimental synthesis, with gaps and Curie temperatures large enough to approach room-temperature operation. A second and overlapping thrust will be on the theory and calculation of materials properties that involve macroscopic orbital currents, including bulk and surface anomalous Hall effects, orbital magnetization, and orbital magnetoelectric couplings. As a cross-cutting theme, computational materials search strategies will be used to identify promising candidate materials and structures that may exhibit the desired topological or magnetoelectric properties, especially including two-dimensional Chern-insulator states at surfaces of normal magnetic insulators and their interfaces with time-reversal-invariant topological insulators.The project will lead to the development of algorithms that will ultimately be implemented in open-source code packages and made available to the wider electronic-structure community. It will also contribute to the development of novel materials that are promising for commercial applications, especially ones involving the coupling of electrical and magnetic responses. Training and mentorship of junior researchers (graduate students and postdocs) will take place, contributing to scientific workforce development.

非技术摘要在过去的二十年中，人们越来越多地认识到，来自差异几何和拓扑的某些数学概念有时是对晶体固体中电子行为的理解的核心。 电子用量子力学波函数描述，这些电子的动量变化的方式编码了许多有关固体的信息，尤其是其电气和磁反应以及它们相互耦合。 当波形在动量空间中扭曲时，这会导致所谓的“拓扑绝缘子”状态，这是过去十年中强烈研究兴趣的重点。从定义上讲，电流不能在绝缘子的内部流动，但是拓扑绝缘子具有不寻常的特性，即在表面上保证有电流通道。 本研究计划旨在进一步发展这种效果的形式理论，旨在发明用于计算固体相关属性的强大而有效的计算算法，并对显示新属性或增强属性的材料进行计算搜索。该项目将导致开发算法，这些算法最终将在开源代码软件包中实施，并提供给更广泛的电子结构社区。 它还将有助于开发新型材料，这些材料有望成为商业应用，尤其是涉及电气和磁反应耦合的材料。初级研究人员（研究生和博士后）的培训和指导将有助于科学劳动力发展。技术摘要这项研究计划的重点是拓扑绝缘子或其他轨道电流的电子特性，其中发挥了重要作用。目的是（i）进一步发展这种系统的形式理论，利用来自差异几何形状的浆果阶段，浆果曲率和Chern数的数学概念； （ii）发明与这些数学概念相关的计算材料属性的准确有效的计算方法； （iii）使用计算方法来识别有希望的新材料或结构，在这些材料或结构中可以表现出自己，这可能会导致技术应用。尽管最近的许多工作集中在诸如BI2SE3之类的时间反转拓扑绝缘子上，但此处的重点将放在量子异常的大厅或Chern绝缘子，轴突绝缘子和Weyl Semimetals上，其中时间逆转的配音自发地破裂。尽管25年前已经指出了Chern-uslator状态的可能性，但它直到最近才通过实验证明，并且仅在低温下进行证明。将制定策略，用于从理论上识别可通过实验合成的二维Chern-Chern-undunmulator状态，而间隙和居里温度足够大，可以接近室温操作。第二个和重叠的推力将取决于涉及宏观轨道电流的材料特性的理论和计算，包括散装和表面异常的霍尔效应，轨道磁化以及轨道磁电耦合。 As a cross-cutting theme, computational materials search strategies will be used to identify promising candidate materials and structures that may exhibit the desired topological or magnetoelectric properties, especially including two-dimensional Chern-insulator states at surfaces of normal magnetic insulators and their interfaces with time-reversal-invariant topological insulators.The project will lead to the development of algorithms that will ultimately be implemented in open-source code包装并提供给更广泛的电子结构社区。 它还将有助于开发新型材料，这些材料有望成为商业应用，尤其是涉及电气和磁反应耦合的材料。初级研究人员（研究生和博士后）的培训和指导将有助于科学劳动力发展。