Decoding Spatial Complexity in Strongly Correlated Electronic Systems

该奖项支持理论和计算研究，以及关于电子之间强相互作用的材料的教育，这些相互作用导致材料中电子运动的强相关性。在金属和半导体等传统材料中，电子均匀分布，就像西红柿汤填充容器一样。但这些强相关材料内部的电子更像是一种奇异的秋葵汤：纳米级图像显示，电子在表面聚集成复杂的形状。这些模式和它们的形成可能是理解强相关材料不寻常的电子特性特征的关键，并最终掌握这些材料导致技术应用。大多数理论和实验工具都是为理解和检测均匀电子状态而设计的，因此有必要设想和探索新的框架，以理解为什么在强相关材料中电子分布中形成模式。结合分形数学和无序材料的统计力学的理论工具，PI旨在开发新的概念和方法来解释和理解这些材料的纳米级电子结构。纳米尺度比人类头发的直径还要小20万倍。该项目旨在开发她引入该领域的几何聚类分析技术，以便更好地理解和最终控制这些材料，从而使它们能够成功地应用于市场。PI将继续发展她开始的指导项目，该项目针对的是她所在大学物理专业的女研究生。PI还将继续访问K-12公立学校，讨论她的研究。这种拓展结合了互动的动手超导和磁性演示与教育有关当前凝聚态研究。此外，建议的工作还将促进一名研究生的培养。该奖项支持理论和计算研究，以及强相关电子材料的教育，旨在促进对电子不均匀分布形成的模式的理解。越来越多的实验证据表明，许多强相关的电子系统，如镍酸盐、铜酸盐和锰酸盐，在局部电子性质上表现出纳米级的变化。描述这些材料的电子行为涉及多个自由度，包括轨道、自旋、电荷和晶格自由度。与无序的相互作用增加了另一个维度：无序不仅可以破坏相变，在尾迹中留下纯粹的交叉；它可以从根本上改变基态，通常禁止长距离秩序。特别是在不同的有序物理倾向竞争的系统中，无序可以为竞争的基态提供成核点，从而导致空间格局的形成和复杂性。许多自由度的相互作用、强相关性和无序性可以导致长度尺度的层次结构和纳米尺度上的模式形成。有必要设计和开发新的方法来理解、检测和表征强相关电子材料中的电子模式形成，特别是在存在严重无序效应的情况下。由此产生的理论指导将使许多材料的理论和实验之间更加直接的联系，并为理解强相关材料相图的“争议”区域提供了一条前进的道路。PI的目标是进一步发展她在强相关电子系统领域开创的几何聚类分析技术，以便最大限度地利用这些方法从实验中提取信息，并促进这些技术在各种材料和图像探针中的广泛应用。为了做到这一点，PI将通过数值模拟在随机伊辛模型中发展几何临界理论。由此产生的工作预计将与几种实验技术相结合，并产生新的数据采集和分析模式，以及能够检测和表征物质新相的新方法。PI将继续发展她开始的指导项目，该项目针对的是她所在大学物理专业的女研究生。PI还将继续访问K-12公立学校，讨论她的研究。这种拓展结合了互动的动手超导和磁性演示与教育有关当前凝聚态研究。此外，建议的工作还将促进一名研究生的培养。

NON-TECHNICAL SUMMARYThis award supports theoretical and computational research, and education on materials with strong interactions among electrons which lead to strong correlations in the motions of electrons in the material. Inside conventional materials like metals and semiconductors, the electrons are evenly spread out, like tomato soup filling a container. But the electrons inside these strongly correlated materials act more like an exotic gumbo: nanoscale images show that the electrons clump into complicated shapes at the surface. These patterns and their formation may be a key to understanding the unusual electronic properties characteristic of strongly correlated materials and to the eventual mastery of these materials leading to technological applications. Most theoretical and experimental tools are designed for understanding and detecting homogeneous electronic states, and it is necessary to envision and explore new frameworks for understanding why patterns form in the distribution of electrons in strongly correlated materials. Combining theoretical tools from fractal mathematics and the statistical mechanics of disordered materials, the PI aims to develop new concepts and methods for interpreting and understanding the nanoscale electronic textures of these materials. The nanoscale is about two hundred thousand times smaller than the diameter of a human hair. The PI aims to develop geometric cluster analysis techniques that she introduced into the field, in order to better understand and eventually control these materials so that they can be successfully applied in the marketplace. The PI will continue to develop the mentoring program she began for graduate women in the physics program at her home institution. The PI will also continue to visit K-12 public schools to discuss her research. This outreach combines interactive hands-on superconductivity and magnetism demonstrations with education about current condensed matter research. In addition, the proposed work will also advance the training of one graduate student.TECHNICAL SUMMARYThis award supports theoretical and computational research, and education on strongly correlated electron materials with an aim to advance understanding of patterns formed by inhomogeneous distribution of electrons. There is growing experimental evidence that many strongly correlated electronic systems such as nickelates, cuprates, and manganites exhibit nanoscale variations in local electronic properties. Describing the electronic behavior of these materials involves multiple degrees of freedom, including orbital, spin, charge, and lattice degrees of freedom. The interplay with disorder adds another dimension: not only can disorder destroy phase transitions, leaving mere crossovers in the wake; it can fundamentally alter ground states, often forbidding long range order. Especially in systems where different physical tendencies to order compete, disorder can provide nucleation points for competing ground states, leading to spatial pattern formation and complexity. The interplay of many degrees of freedom, strong correlations, and disorder can lead to a hierarchy of length scales and to pattern formation at the nanoscale. There is a need to design and develop new ways of understanding, detecting, and characterizing electronic pattern formation in strongly correlated electronic materials, especially in the presence of severe disorder effects. Resulting theoretical guidance will enable more direct contact between theory and experiment for a number of materials, and provide a path forward for understanding "disputed" regions of phase diagrams of strongly correlated materials. The PI aims to further develop the geometric cluster analysis techniques that she pioneered in the field of strongly correlated electronic systems, in order to maximize the information that can be extracted from experiments using these methods, and to facilitate the broad application of these techniques to various materials and image probes. In order to do this, the PI will develop theory of geometric criticality in random Ising models through numerical simulations. The resulting work is expected to connect to several experimental techniques and to yield new modes of data taking and analysis, and new methods enabling the detection and characterization of novel phases of matter.The PI will continue to develop the mentoring program she began for graduate women in the physics program at her home institution. The PI will also continue to visit K-12 public schools to discuss her research. This outreach combines interactive hands-on superconductivity and magnetism demonstrations with education about current condensed matter research. In addition, the proposed work will also advance the training of one graduate student.