Correlated Solid and Liquid States in High Magnetic Fields

非技术总结该奖项支持对物质的新的电子态的理论研究和教育，这种新的电子态是由电子之间的相互作用引起的相关运动产生的。对出射态的理解是现代凝聚态物理学中的一个重要挑战。电子系统被限制在半导体之间界面的平面上，已被证明对于研究新的物质状态是有利的，在强磁场的作用下产生了各种各样的物质。该奖项支持对液晶和晶体相的性质、自旋的作用--电子的一种量子力学性质--以及受限环境对电子的影响的研究。PI将对压缩性进行详细计算，这是一个重要的热力学量，包含了非平凡的多体效应，并探索其他理论方法对非均匀分数量子霍尔态的适用性。这项研究为支持新技术和教育的知识库做出了贡献。对分数量子霍尔效应在不同背景下的研究带来了新的发现和新的想法，如拓扑绝缘体、陈绝缘体、Majorana费米子、阿贝尔和非阿贝尔任意子，以及操纵类似量子霍尔态或拓扑态进行计算的想法。分数量子霍尔效应的研究也一直是半导体材料质量提高的动力，而半导体材料是其他技术创新所必需的。这笔助学金资助的研究生将在前沿研究领域接受广泛的培训，一方面掌握凝聚态理论和计算方法，另一方面接触国际合作研究。PI和参与该项目的学生将投入一部分时间与初中、高中和本科生合作，让他们接触到与低维相关的想法，并激励他们从事物理研究。这将通过宾夕法尼亚州立大学现有的外展活动以及组织暑期学校来实现。技术总结该奖项支持有关二维电子暴露在强磁场中时固体和液体中出现的新现象的理论研究和教育。它将侧重于几个问题，由于近年来发展了非常准确的理论理解，现在可以在这些问题上取得实质性进展。一些具体项目如下。最低朗道能级的晶体被证明是一种非平凡的、固有的量子力学状态，它具有称为气泡间隙的非平凡缺陷。晶体的自旋物理将使用理论方法和蒙特卡罗模拟进行研究。PI将研究强关联在气泡晶体中的作用，据信气泡晶体发生在第二朗道能级。最近对各向异性有效质量作用的理解将扩展到更多种类的分数态。相关系统的可压缩性将作为填充因子的函数来计算，其中包含了液态和晶态的变化。将探索密度泛函理论等方法对描述非均匀情况的适用性。这些问题与在半导体异质结和石墨烯二维系统上进行的实验有关。在所有这些情况下，目的将是获得作为各种参数的函数的详细的定量预测，例如朗道能级混合和横向波函数的宽度和形状，这些参数可以在实验中以可控的方式改变。将根据需要使用分析方法、精确对角化和蒙特卡罗技术的组合。这项资助支持的研究生将在前沿研究领域接受广泛的培训，一方面掌握凝聚态理论和计算方法，另一方面接触国际合作研究。PI和参与该项目的学生将投入一部分时间与初中、高中和本科生合作，让他们接触到与低维相关的想法，并激励他们从事物理研究。这将通过宾夕法尼亚州立大学现有的外联活动以及举办暑期学校来实现。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on new electronic states of matter that emerge from correlated motion of electrons that arise from the interactions among them. The understanding of emergent states is an important challenge in modern condensed matter physics. The system of electrons confined to a plane at an interface between semiconductors has proved to be fertile for the investigation of new states of matter, producing a large variety under the application of a high magnetic field. This award supports research that will provide insight into the nature of liquid and crystal phases, the role of spin - a quantum mechanical property of the electron, and effects of the confined environment on electrons. The PI will perform detailed calculations of compressibility, an important thermodynamic quantity, incorporating nontrivial many body effects, and also explore the applicability of other theoretical methods, to non-uniform fractional quantum Hall states. This research contributes to the knowledgebase that supports new technology and to education. The study of the fractional quantum Hall effect in various contexts has led to new discoveries and new ideas, such as topological insulators, Chern insulators, Majorana fermions, abelian and non-abelian anyons, and the idea of manipulating quantum-Hall-like, or topological, states to perform computation. The study of fractional quantum Hall effect has also been a driving force for improvements in the quality of semiconductor materials, necessary for other technological innovations. The graduate students supported by this grant will receive broad training in forefront areas of research, will master condensed matter theory on the one hand and computational methods on the other, and will be exposed to international collaborative research. The PI and students involved in the project will devote a portion of their time to working with middle school, high school and undergraduate students to expose them to ideas that become relevant in low dimensions, and to motivate them into physics research. This will be done through existing outreach activities at Penn State as well as through organization of a summer school.TECHNICAL SUMMARYThis award supports theoretical research and education concerning new phenomena in solid and liquid phases that occur when two-dimensional electrons are exposed to a strong magnetic field. It will focus on several problems on which substantial progress can now be made as a result of the very accurate theoretical understanding that has been developed in recent years. Some of the specific projects are as follows. The crystal in the lowest Landau level has been shown to be a nontrivial, inherently quantum mechanical state, which has non-trivial defects called bubble interstitials. The spin physics of the crystal will be studied using theoretical methods as well as Monte Carlo simulation. The PI will investigate the role of strong correlations in the bubble crystal believed to occur in the second Landau level. The recent understanding of the role of anisotropic effective mass will be extended to a larger variety of fractional states. The compressibility of the correlated system will be calculated as a function of the filling factor, incorporating the variety of liquid and crystal states. The applicability of methods such as the density functional theory will be explored to describe non-homogeneous situations. These questions are of relevance to experiments being performed on semiconductor heterojunction and graphene two-dimensional systems. In all of these cases, the aim will be to obtain detailed quantitative predictions as a function of various parameters, such as Landau level mixing and the width and shape of the transverse wave function, which can be varied in experiments in a controllable manner. A combination of analytical methods, exact diagonalization and Monte Carlo techniques will be used as needed.The graduate students supported by this grant will receive broad training in forefront areas of research, will master condensed matter theory on the one hand and computational methods on the other, and will be exposed to international collaborative research. The PI and students involved in the project will devote a portion of their time to working with middle school, high school and undergraduate students to expose them to ideas that become relevant in low dimensions, and to motivate them into physics research. This will be done through existing outreach activities at Penn State as well as through organization of a summer school.