RUI: Highly Correlated Systems of Reduced Dimensionality: Broken Symmetry Phases in Quantum Hall Systems

RUI：高度相关的降维系统：量子霍尔系统中的破缺对称相

• 批准号: 0086191
• 负责人: Edward Rezayi
• 金额: --
• 依托单位: California State University-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-11-15 至 2004-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0086191&HistoricalAwards=false
• 关键词: RUI; Highly; Correlated; Systems; Reduced

0086191RezayiThis is a RUI (Research at Undergraduate Institution) award for theoretical reseach on highly correlated electrons in reduced dimensionality. Electrons confined to two-dimensional Landau levels exhibit a host of intriguing phenomena. The most notable of these is the fractional quantum Hall effect. An emerging area in quantum Hall systems is the physics of high Landau levels. Experiments show highly anisotropic and non-linear electronic transport coefficients, as well as a reentrant quantum Hall phase showing a conduction threshold. These unusual transport properties have been associated with translational symmetry-breaking phases of the two-dimensional electron gas as predicted by Koulakov, Fogler and Shklovskii and also by Moessner and Chalker. The anisotropic transport results from a striped phase and the reentrant behavior could be a signature of a pinned crystalline phase. These are different from Wigner solids in having more than one electron per unit cell. The research projects to be done here are extensive studies of these phases by numerical exact-diagonalization methods. This approach seems particularly promising as the broken-symmetry phases have already been detected using such techniques by the principal investigator, Duncan Haldane and Kun Yang. Another area of research is to study various excitations (particularly involving reversed spins) of the quantum Hall state observed at half-filling of the first excited Landau level. Recent numerical calculations by the principal investigator and Duncan Haldane favor a BCS-like spin-polarized ground state of p-wave pairing of composite fermions - a composite object made up of an electron and an attached magnetic flux carrying two units of flux quanta. Upon tilting the magnetic field towards the electron-layer, a transition to a striped phase with associated anisotropic transport has been seen experimentally. The nature of this transition, as well as the quantitative dependence of physical properties (such as the energy gap) on the tilt angle, will also be investigated. In addition, the relevance of recently proposed novel quantum Hall phases involving groupings (generalized pairings) of more than two electrons to states of the first excited Landau level will be investigated. Many of these projects involve three important phases of electronic matter: the Fermi liquid, BCS-type pairing, and charge-density wave states. The work is therefore likely to enhance and deepen our understanding of these important phases of matter and uncover important inter-relations among them.%%% This is a RUI (Research at Undergraduate Institution) award for theoretical reseach on highly correlated electrons in reduced dimensionality. Electrons confined to two-dimensional Landau levels exhibit a host of intriguing phenomena. The most notable of these is the fractional quantum Hall effect. A number of different projects will be undertaken in this field, primarily using numerical methods. Undergraduate students will participate in some phases of the research.***

0086191 Rezayi这是一个RUI（研究在本科院校）奖的理论研究高度相关的电子在减少的维度。局限于二维朗道能级的电子表现出许多有趣的现象。其中最著名的是分数量子霍尔效应。量子霍尔系统的一个新兴领域是高朗道能级物理学。实验表明，高度各向异性和非线性的电子输运系数，以及一个可重入的量子霍尔相位显示的导电阈值。这些不寻常的输运性质与Koulakov，Fogler和Shklovskii以及Moessner和Chalker预测的二维电子气的平移破缺相有关。各向异性输运的结果从条纹相和重入的行为可能是一个钉扎结晶相的签名。它们与维格纳固体的不同之处在于每个晶胞中有一个以上的电子。这里要做的研究项目是通过数值精确对角化方法对这些阶段进行广泛的研究。这种方法似乎特别有希望，因为主要研究者邓肯·哈勒和杨昆已经使用这种技术检测到了对称性破坏阶段。另一个研究领域是研究在第一个受激朗道能级半满时观察到的量子霍尔态的各种激发（特别是涉及反向自旋）。最近由首席研究员和邓肯·哈拉格斯进行的数值计算支持复合费米子p波配对的BCS样自旋极化基态--复合费米子是由一个电子和一个携带两个单位通量量子的附加磁通量组成的复合物体。在倾斜的磁场对电子层，过渡到条纹相与相关的各向异性运输已被实验观察到。这种过渡的性质，以及对倾斜角的物理性质（如能隙）的定量依赖性，也将被调查。此外，最近提出的新的量子霍尔相位涉及分组（广义配对）的两个以上的电子的第一激发朗道级的状态的相关性将进行调查。其中许多项目涉及电子物质的三个重要阶段：费米液体，BCS型配对和电荷密度波态。因此，这项工作可能会增强和加深我们对这些重要的物质阶段的理解，并揭示它们之间重要的相互关系。这是一个RUI（研究在本科院校）奖的理论研究高度相关的电子在减少维。局限于二维朗道能级的电子表现出许多有趣的现象。其中最著名的是分数量子霍尔效应。将在这一领域开展一些不同的项目，主要使用数字方法。本科生将参与研究的某些阶段。***