Correlated Solid and Liquid States in High Magnetic Fields

非技术性总结该奖项支持理论研究和教育的新的电子状态的物质，出现从相关运动的电子，从它们之间的相互作用。对突现态的理解是现代凝聚态物理学的一个重要挑战。被限制在半导体界面上的电子系统已被证明是研究新物质状态的肥沃土壤，在高磁场的作用下产生了大量的变化。该奖项支持的研究将提供洞察液体和晶体相的性质，自旋的作用-电子的量子力学性质，以及受限环境对电子的影响。PI将进行详细的计算压缩性，一个重要的热力学量，结合非平凡的许多身体的影响，并探讨其他理论方法的适用性，非均匀的分数量子霍尔态。这项研究有助于支持新技术和教育的知识库。分数量子霍尔效应在不同背景下的研究导致了新的发现和新的想法，如拓扑绝缘体，陈省身绝缘体，马约拉纳费米子，阿贝尔和非阿贝尔任意子，以及操纵量子霍尔或拓扑状态来执行计算的想法。分数量子霍尔效应的研究也是半导体材料质量改进的驱动力，这是其他技术创新所必需的。该补助金支持的研究生将在研究的前沿领域接受广泛的培训，一方面将掌握凝聚态理论，另一方面将掌握计算方法，并将接触国际合作研究。参与该项目的PI和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度相关的想法，并激励他们进行物理研究。这将通过在宾夕法尼亚州立大学现有的推广活动，以及通过组织暑期学校来完成。技术总结该奖项支持理论研究和教育有关的新现象，在固体和液体相时发生的二维电子暴露在一个强磁场。它将集中在几个问题上，由于近年来发展起来的非常准确的理论理解，现在可以取得实质性进展。一些具体项目如下。在最低的朗道能级的晶体已被证明是一个非平凡的，固有的量子力学状态，它有非平凡的缺陷称为泡状晶体。晶体的自旋物理将使用理论方法以及蒙特卡罗模拟进行研究。PI将研究被认为发生在第二个朗道水平的气泡晶体中强相关性的作用。最近对各向异性有效质量的作用的理解将扩展到更大范围的分数态。相关系统的可压缩性将作为填充因子的函数来计算，并结合各种液晶和晶体状态。将探讨密度泛函理论等方法的适用性，以描述非均匀的情况。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，目标将是获得详细的定量预测作为各种参数的函数，如朗道能级混合和横波函数的宽度和形状，这可以在实验中以可控的方式变化。根据需要，将使用分析方法、精确对角化和蒙特卡罗技术相结合。获得该资助的研究生将接受前沿研究领域的广泛培训，一方面掌握凝聚态理论，另一方面掌握计算方法，并将接触国际合作研究。参与该项目的PI和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度相关的想法，并激励他们进行物理研究。这将通过宾夕法尼亚州立大学现有的外联活动以及通过组织暑期学校来实现。

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.