Theory and Application of Berry Phase Methods in Solids

材料研究部和网络基础设施办公室为该奖项提供资金。它支持理论研究和教育的新材料的电子特性，其中轨道电流发挥重要作用。 其目标是（i）开发此类系统的形式理论，利用微分几何的数学概念;（ii）开发准确，高效，稳健和信息丰富的算法来计算材料的相关属性;以及（iii）应用这些方法来研究实际和尚未合成的材料，特别是具有潜在技术应用的材料。该研究计划的一个主要目标是进一步发展时间反演对称性被破坏的材料的电子结构理论，例如铁磁体，以及拓扑绝缘体理论。 数学方法相关的Berry阶段和Wannier表示将被用来调查这些更普遍的问题。 这些技术已被证明是有用的理解电极化，轨道磁化，和异常的霍尔电导率。理论研究将进行，以更好地了解两类拓扑绝缘体。第一种是理论上更简单但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后20年左右，还没有已知的实验实现。这项工作应该澄清这些材料的预期物理特性，并可能为实验研究提出进一步的途径。 第二种是“Z2拓扑绝缘体”，在过去的五年里已经发现了几个例子。 研究计划的第二个主要目标是计算晶体绝缘体的线性磁电耦合。 这种计算方法仍处于初期阶段，但进一步发展的时机已经成熟。 使用第一原理的方法，所有的各种贡献的磁电耦合将被计算，包括纯电子，晶格位移介导的，应变介导的，几个原型材料。 该项目预计将导致在理解具有不寻常的磁性或拓扑顺序的材料的电子结构方面取得根本性进展，并有助于开发有希望用于商业应用的新材料，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，使这些材料的属性的第一原理计算。材料研究部和网络基础设施办公室为该奖项提供资金。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发挥重要作用的新材料。 磁现象通常分为两类：一类是由电子的量子力学性质（称为自旋）解释的，另一类是与原子尺度下流动的微观电流有关的。 这些后一种"轨道电流"的影响有时是次要的。对于铁等普通磁铁，它们的磁性不到10%。然而，近年来，人们对某些轨道电流起主导作用的新材料产生了浓厚的兴趣。 例如，在几年前的一系列引人注目的发展中，“拓扑绝缘体”的理论预测很快得到了实验的证实。根据定义，电流不能在绝缘体的内部流动，但拓扑绝缘体具有不寻常的特性，即在表面保证有载流通道。基本上，电子在体块中的"拓扑"组织强制了原子尺度轨道电流的某种对应组织，以便在表面产生净电流。这种现象可能具有重要的实际应用;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的计划侧重于获得这些不寻常的材料及其磁电现象的详细了解，活动范围包括正式理论，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。

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.