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

0086191 rezayi这是一项本科院校研究奖，用于对低维高度相关电子的理论研究。局限于二维朗道能级的电子表现出许多有趣的现象。其中最引人注目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。实验显示出高度各向异性和非线性的电子输运系数，以及具有传导阈值的可重入量子霍尔相。正如Koulakov， Fogler和Shklovskii以及Moessner和Chalker所预测的那样，这些不寻常的输运性质与二维电子气体的平移对称破缺相有关。各向异性输运是由条纹相引起的，重入行为可能是固定晶相的标志。这些固体与维格纳固体的不同之处在于每个单位电池有一个以上的电子。这里要做的研究项目是用数值精确对角化方法对这些相进行广泛的研究。这种方法似乎特别有希望，因为首席研究员邓肯·霍尔丹（Duncan Haldane）和杨坤（Kun Yang）已经用这种技术检测到了非对称相位。另一个研究领域是研究在第一激发朗道能级半填充时观察到的量子霍尔态的各种激发（特别是涉及反向自旋的激发）。首席研究员和邓肯·霍尔丹最近的数值计算支持复合费米子p波对的bcs -类自旋极化基态，复合费米子是一种复合物体，由一个电子和一个附加的磁通量组成，携带两个单位的通量量子。当磁场向电子层倾斜时，在实验中观察到条纹相与相关的各向异性输运的转变。这种转变的性质，以及物理性质（如能隙）对倾斜角的定量依赖，也将被研究。此外，将研究最近提出的涉及两个以上电子分组（广义配对）的新型量子霍尔相与第一激发态朗道能级的相关性。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物质这些重要阶段的理解，并揭示它们之间的重要相互关系。%%%这是一个RUI（本科院校研究）奖，用于对低维高度相关电子的理论研究。局限于二维朗道能级的电子表现出许多有趣的现象。其中最引人注目的是分数量子霍尔效应。将在这一领域开展若干不同的项目，主要使用数值方法。本科生将参与研究的某些阶段

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.***