Electronic Fractals in Strongly Correlated Quantum Materials

强相关量子材料中的电子分形

• 批准号: 2006192
• 负责人: Erica Carlson
• 金额: $ 33万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2006192&HistoricalAwards=false
• 关键词: Electronic; Fractals; Strongly; Correlated; Quantum

NONTECHNICAL SUMMARYThis award supports theoretical research on refining and extending techniques aimed at maximizing the information that can be extracted from experiments performed on strongly correlated electronic materials. The fragility and complexity of ice crystals and trees have found their counterparts in strongly correlated electronic materials. Inside conventional metals and semiconductors, electrons are typically evenly spread out, like liquid filling a container. But in correlated quantum materials, where electrons interact strongly with each other and with the atomic nuclei of the material, electrons act more like an exotic gumbo. Nanoscale images of the surfaces of these materials show that the electrons clump into complicated shapes, at least at the surface. Understanding the formation of these patterns is vital to our understanding of the electronic properties and to our eventual technological control of these materials. The PI has defined new paradigms for interpreting and understanding nanoscale electronic textures observed at the surface of these materials. These new analysis methods allow conclusions to be drawn about the inside of a material, based on observations that are made only on the outside of the material. The key insight is that the geometric structure of fractals reveals the dimension in which they reside: Fractals have different shapes when they form only on the surface of a material (like frost on a window), from when the fractals extend deep inside the material (like a tree whose roots reach deep underground). This new field of analysis has revealed universal behavior across several families of strongly correlated electronic materials. The PI proposes to uncover why these patterns are so ubiquitous at the surface of correlated materials. This award also supports the PI's educational and outreach activities. The PI continues to be a popularizer of science. She has already produced the YouTube channel www.youtube.com/profcarlson (with over 65,000 views) which has made her lectures on introductory electricity and magnetism freely available, as well as the popular video series, “Understanding the Quantum World,” with The Great Courses. The PI will start a YouTube channel for the Purdue Quantum Science and Engineering Instutite, and also produce a second video series with The Great Courses, on Quantum Materials. TECHNICAL SUMMARYThis award supports theoretical research that is aimed at refining and extending the geometric cluster analysis technique pioneered by the PI in the field of strongly correlated electronic systems, in order to maximize the information that can be extracted from experiments using the PI's new methods, and to facilitate the broad application of these techniques to various materials and image probes. In order to do this, the PI will advance the theory of geometric criticality in clean and random Ising models, via numerical simulations. At the successful completion of these calculations, several conventional (and widely available) experimental techniques will have at their disposal new modes of datataking and analysis and new methods enabling the detection and characterization of novel phases of matter.These studies are transformational in that the PI is importing concepts and techniques from fractal mathematics and disordered statistical mechanics into the field of correlated quantum materials in order to better understand fractal electronic pattern formation and its impact on these materials. The successful implementation of these ideas is expected to continue to have potentially important impact in several correlated quantum materials, including cuprate and iron pnictide superconductors, manganites, nickelates, cobaltates, and vanadium oxides.This award also supports the PI's educational and outreach activities. The PI continues to be a popularizer of science. She has already produced the YouTube channel www.youtube.com/profcarlson (with over 65,000 views) which has made her lectures on introductory electricity and magnetism freely available, as well as the popular video series, “Understanding the Quantum World,” with The Great Courses. The PI will start a YouTube channel for the Purdue Quantum Science and Engineering Instutite, and also produce a second video series with The Great Courses, on Quantum Materials.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术性总结该奖项支持理论研究的精炼和扩展技术，旨在最大限度地提高信息，可以从强相关的电子材料进行的实验中提取。冰晶和树木的脆弱性和复杂性在强相关的电子材料中找到了对应物。在传统的金属和半导体内部，电子通常是均匀分布的，就像液体填充容器一样。但在相关量子材料中，电子彼此之间以及与材料的原子核之间都有强烈的相互作用，电子的行为更像是一种异国情调的秋葵汤。这些材料表面的纳米级图像显示，电子聚集成复杂的形状，至少在表面是这样。 理解这些图案的形成对于我们理解电子特性和我们最终对这些材料的技术控制至关重要。PI已经定义了解释和理解在这些材料表面观察到的纳米级电子纹理的新范例。 这些新的分析方法允许基于仅在材料外部进行的观察得出关于材料内部的结论。 关键的见解是，分形的几何结构揭示了它们所处的维度：当分形仅在材料表面形成时（如窗户上的霜），分形具有不同的形状，当分形深入材料内部时（如树根深入地下的树）。这一新的分析领域揭示了几个强相关电子材料家族的普遍行为。PI建议揭示为什么这些图案在相关材料的表面如此普遍。该奖项还支持PI的教育和推广活动。PI仍然是科学的普及者。 她已经制作了YouTube频道www.youtube.com/profcarlson（观看次数超过65，000次），免费提供她关于电和磁的介绍性讲座，以及流行的视频系列“理解量子世界”。 PI将为普渡大学量子科学与工程学院开设一个YouTube频道，并制作第二个关于量子材料的视频系列。 技术总结该奖项支持旨在完善和扩展PI在强相关电子系统领域开创的几何聚类分析技术的理论研究，以最大限度地利用PI的新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将通过数值模拟推进清洁和随机伊辛模型的几何临界理论。 在成功完成这些计算后，几种常规（广泛提供）实验技术将拥有新的数据记录和分析模式，以及能够检测和表征物质新相的新方法。这些研究是变革性的，因为PI正在将分形数学和无序统计力学的概念和技术引入相关量子材料领域，以更好地理解分形电子图案的形成及其对这些材料的影响。 这些想法的成功实施预计将继续对几种相关量子材料产生潜在的重要影响，包括铜酸盐和铁磷属元素化物超导体，锰氧化物，镍酸盐，钴酸盐和钒氧化物。该奖项还支持PI的教育和推广活动。PI仍然是科学的普及者。 她已经制作了YouTube频道www.youtube.com/profcarlson（观看次数超过65，000次），免费提供她关于电和磁的介绍性讲座，以及流行的视频系列“理解量子世界”。 PI将为普渡大学量子科学与工程学院开设一个YouTube频道，并与The Great Courses一起制作第二个关于量子材料的视频系列。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Period multiplication cascade at the order-by-disorder transition in uniaxial random field XY magnets

单轴随机场 XY 磁体中有序无序转变的周期倍增级联

• DOI: 10.1038/s41467-020-18270-6
• 发表时间: 2020
• 期刊: Nature Communications
• 影响因子: 16.6
• 作者: Basak, S.;Dahmen, K. A.;Carlson, E. W.
• 通讯作者: Carlson, E. W.

Connecting Complex Electronic Pattern Formation to Critical Exponents

将复杂的电子模式形成与关键指数联系起来

• DOI: 10.3390/condmat6040039
• 发表时间: 2021
• 期刊: Condensed Matter
• 影响因子: 1.7
• 作者: Liu, Shuo;Carlson, Erica W.;Dahmen, Karin A.
• 通讯作者: Dahmen, Karin A.

Deep learning Hamiltonians from disordered image data in quantum materials

• DOI: 10.1103/physrevb.107.205121
• 发表时间: 2023-05-10
• 期刊: PHYSICAL REVIEW B
• 影响因子: 3.7
• 作者: Basak, S.;Banguero, M. Alzate;Carlson, E. W.
• 通讯作者: Carlson, E. W.