Theory and Application of Berry Phase Methods in Solids

固体浆果相法的理论与应用

• 批准号: 1005838
• 负责人: David Vanderbilt
• 金额: $ 50.4万
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005838&HistoricalAwards=false
• 关键词: Theory; Application; Berry; Phase; Methods

TECHNICAL SUMMARY The Division of Materials Research and the Office of Cyberinfrastrcture contribute funds to this award. It supports theoretical research and education on the electronic properties of novel materials in which orbital currents play an important role. The objectives are (i) to develop the formal theory of such systems, making use of mathematical concepts from differential geometry; (ii) to develop accurate, efficient, robust and informative algorithms for computing the associated properties of materials; and (iii) to apply these methods to study actual and as-yet unsynthesized materials, especially ones having potential technological applications. A major thrust of the research program is to make further developments in the theory of the electronic structure of materials in which time-reversal symmetry is broken, for example ferromagnets, and in the theory of topological insulators. Mathematical approaches related to Berry phases and the Wannier representation will be utilized to investigate these more general problems. These techniques have proven useful for understanding electric polarization, orbital magnetization, and the anomalous Hall conductivity. Theoretical investigations will be carried out to better understand two classes of topological insulators. The first is the theoretically simpler but experimentally more elusive "Chern" or "quantum anomalous Hall" insulator, of which no known experimental realizations exist to date some 20 years after a theory describing them appeared. This work should clarify the expected physical properties of such materials and may suggest further avenues for experimental searches. The second are the "Z2 topological insulators," several examples of which have been discovered in the last five years. A second major thrust of the research program concerns the calculation of the linear magnetoelectric couplings of crystalline insulators. Methods for such calculations are still in their infancy, but are ripe for further development. Using first-principles methods, all of the various contributions to the magnetoelectric coupling will be calculated, including purely electronic, lattice-displacement-mediated, and strain-mediated ones, for several prototypical materials. This project is expected to lead to fundamental advances in the understanding of the electronic structure of materials with unusual magnetic or topological order, and to contribute to the development of novel materials that are promising for commercial applications, especially ones involving the coupling of electrical and magnetic responses. This project will also contribute to developing formal theory and methods to enable first principles calculations of the properties of these materials. NON-TECHNICAL SUMMARY The Division of Materials Research and the Office of Cyberinfrastrcture contribute funds to this award. It supports research and education in computational condensed-matter theory, with a focus on obtaining a deeper understanding of novel materials in which orbital currents play an essential role. Magnetic phenomena generally fall into two classes: those explained by a quantum mechanical property of the electron known as spin, and those related to the presence of microscopic currents that flow at the atomic scale. The effects of these latter "orbital currents" are sometimes secondary. For ordinary magnets such as iron, they account for less than 10% of the magnetism. However, in recent years there has been an outpouring of interest in certain novel materials for which the orbital currents play the dominant role. In a series of remarkable developments a few years ago, for example, theoretical predictions of "topological insulators" were quickly followed by experimental confirmations. 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. Essentially, the "topological" organization of the electrons in the bulk enforces a certain corresponding organization of the atomic-scale orbital currents so as to produce a net current at the surface. Such phenomena could have important practical applications; one example might be materials that can convert electrical impulses to magnetic impulses and vice versa. The PI's program is focused on obtaining a detailed understanding of these unusual materials and their magnetoelectric phenomena, with activities spanning from formal theory, development and implementation of new computer algorithms, predictive computer simulations, and pedagogical dissemination of the results.

技术摘要材料研究司和数字基础设施办公室为这一奖项提供资金。它支持对轨道电流起重要作用的新材料的电子性质的理论研究和教育。其目的是(I)利用微分几何中的数学概念，发展这类系统的形式理论；(Ii)开发准确、有效、健壮和信息丰富的算法来计算材料的相关性质；以及(Iii)应用这些方法来研究实际的和尚未合成的材料，特别是那些具有潜在技术应用的材料。该研究计划的一个主要目的是进一步发展时间反转对称性被打破的材料的电子结构理论，例如铁磁体，以及拓扑绝缘体理论。与Berry相和Wannier表示相关的数学方法将被用来研究这些更一般的问题。这些技术已经被证明对理解电极化、轨道磁化和反常的霍尔电导是有用的。为了更好地理解两类拓扑绝缘子，将进行理论研究。第一种是理论上更简单，但在实验上更难以捉摸的“陈”或“量子反常霍尔”绝缘体，在描述它们的理论出现约20年后，到目前为止还没有已知的实验实现。这项工作应该澄清这类材料的预期物理性质，并可能为实验研究提供进一步的途径。第二个是“Z2拓扑绝缘子”，在过去五年中已经发现了几个例子。该研究计划的第二个主要内容涉及晶体绝缘子的线性磁电耦合的计算。这类计算方法仍处于初级阶段，但进一步发展的时机已经成熟。利用第一性原理方法，计算了几种典型材料的磁电耦合的各种贡献，包括纯电子的、晶格位移中介的和应变中介的。这一项目有望在理解具有异常磁性或拓扑有序的材料的电子结构方面取得根本性进展，并有助于开发具有商业应用前景的新型材料，特别是涉及电和磁响应耦合的材料。该项目还将有助于发展正式的理论和方法，以便能够对这些材料的性质进行第一性原理计算。非技术概述材料研究司和网络基础设施办公室为这一奖项提供资金。它支持计算凝聚态理论的研究和教育，重点是更深入地了解轨道电流在其中发挥关键作用的新材料。磁性现象通常分为两类：一类是由电子的自旋量子力学性质解释的，另一类是与原子尺度上流动的微观电流的存在有关的。后一种“轨道流”的影响有时是次要的。对于铁这样的普通磁铁，它们占磁力的比例不到10%。然而，近年来，人们对某些轨道流起主导作用的新型材料表现出了浓厚的兴趣。例如，在几年前的一系列令人瞩目的发展中，“拓扑绝缘体”的理论预测很快得到了实验证实。根据定义，电流不能在绝缘子内部流动，但拓扑绝缘子有一个不同寻常的特性，即表面肯定有载流通道。本质上，块体中电子的“拓扑”组织强制原子尺度轨道电流的某种相应组织，从而在表面产生净电流。这种现象可能会有重要的实际应用；一个例子可能是可以将电脉冲转换为磁脉冲的材料，反之亦然。PI的计划专注于获得对这些不寻常的材料及其磁电现象的详细了解，活动范围从正式理论、新计算机算法的开发和实施、预测性计算机模拟以及结果的教学传播。