Berry-Phase Approaches to Electronic Structure Theory and their Applications

该基金用于材料的电子和介电特性的基础理论研究，特别强调这些特性的计算和分析的新技术的发展。目标是(i)继续发展精确、高效、稳健和信息丰富的算法来计算复杂材料的电子结构，以及（ii）将这些方法应用于研究几个重要的材料系统。提出的工作的一个主要推力将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），以某种方式导致计算这些系统中的轨道磁化，异常霍尔电导率和相关电子特性的新方法。与贝里相和万尼尔表示相关的数学方法，已被证明对理解电极化和处理绝缘体中的轨道磁化有用，将用于研究这些更普遍的问题。首先将应用于流动铁磁体，如Fe， Ni和Co。理论研究也将进行，以更好地理解陈氏绝缘体的物理特性，陈氏绝缘体是一类具有不寻常性质的磁性绝缘体，包括量子化的横向霍尔电导率。第二个重点将涉及晶体绝缘体（主要是非磁性的）的介电特性。将开发方法来绘制能量与极化景观，从而确定给定介电或铁电材料的状态电方程，并使用该信息来确定界面和超晶格中的电边界条件的匹配。极性半导体对太赫兹频率外加电场的非线性动态响应将采用第一性原理方法计算，镁掺杂纤锌矿ZnO的介电和压电特性也将采用第一性原理方法计算。晶格对反铁磁绝缘体介电响应的贡献也将被研究。该项目预计将在理解磁性晶体的电子结构方面取得根本性的进展，特别是在计算轨道磁化和本征异常霍尔电导率等重要性质的算法方面。该项目还将包括制定和测试通过直接应用电场来研究绝缘材料的线性和非线性介电特性的新方法。这些领域处于当前计算电子结构理论能力发展的前沿。更广泛的影响该项目将导致算法的发展，最终将在开源代码包中实现，并提供给更广泛的电子结构社区。它还将有助于开发具有商业应用前景的新材料。最后，对初级研究人员（研究生和博士后）进行培训和指导，为科学劳动力的发展做出贡献。

This grant is for fundamental theoretical research on the electronic and dielectric properties of materials, with special emphasis on the development of novel techniques for the computation and analysis of these properties. The objectives are (i) to continue the development of accurate, efficient, robust and informative algorithms for computing the electronic structure of complex materials, and (ii) to apply these methods to study several important material systems.One major thrust of the proposed work will be to make further developments in the theory of the electronic structure of materials in which time-reversal symmetry is broken (e.g., ferromagnets), in a way that leads to new methods for computing the orbital magnetization, anomalous Hall conductivity, and related electronic properties in these systems. Mathematical approaches related to Berry phases and the Wannier representation, which have proved useful for understanding electric polarization and for treating orbital magnetization in insulators, will be utilized to investigate these more general problems. Applications will be made first to itinerant ferromagnets such as Fe, Ni, and Co. Theoretical investigations will also be carried out to better understandthe physics of Chern insulators, a class of magnetic insulators having unusual properties including a quantized transverse Hall conductivity.A second major thrust will concern the dielectric properties of (mostly non-magnetic) crystalline insulators. Methods will be developed for mapping the energy vs. polarization landscape, and thereby determining the electric equation of state of a given dielectric or ferroelectric material, and for using this information to determine the matching of electrical boundary conditions at interfaces and in superlattices. The non-linear dynamic response of polar semiconductors to a terahertz-frequency applied electric field will be calculated using first-principles methods, as will the dielectric and piezoelectric properties of Mg-doped wurtzite ZnO. The lattice contribution to the dielectric response of antiferromagnetic insulators will also be studied.Intellectual MeritThe project is expected to lead to fundamental advances in the understanding of the electronic structure of magnetic crystals, and in particular, to the development of algorithms for computing such important properties as the orbital magnetization and the intrinsic anomalous Hall conductivity. The project will also include the formulation and testing of novel approaches for studying the linear and nonlinear dielectric properties of insulating materials by direct application of electric fields. These areas are at the forefront of current advances in the capabilities of computational electronic-structure theory.Broader ImpactsThe project will lead to the development of algorithms which 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. Finally, training and mentorship of junior researchers (graduate students and postdocs) will take place, contributing to scientific workforce development.