Hamiltonian Theory of Fractionally Filled Chern Bands, and Disorder in Quantum Hall Ferromagnets

分数填充陈能带的哈密顿理论和量子霍尔铁磁体中的无序

• 批准号: 1306897
• 负责人: Ganpathy Murthy
• 金额: $ 27万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2019-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1306897&HistoricalAwards=false
• 关键词: Hamiltonian; Theory; Fractionally; Filled; Chern

NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed to investigate novel states of electrons. Electrons are generally thought to be indivisible which is true at room temperature and under the conditions under which solid state devices normally operate. Most important to this research are the quantum Hall states, which occur in a two-dimensional sheet of electrons, usually at an artificially engineered interface between semiconductors, cooled to temperatures less than one degree from absolute zero, and placed in an a very strong magnetic field perpendicular to the sheet. In the simplest such state the electron can be thought of as "split" into three objects known as composite fermions. Each composite fermion has a charge one-third that of the electron along with other exotic properties. The charge and other properties of the excitation depend on the particular state. Some of these states offer possible platforms for quantum computing. Conventional, semiconductor quantum Hall states need extreme conditions. In the past decade a new way of potentially realizing such states has been proposed where the environment inside some materials can generate the equivalent of very strong internal magnetic fields. The PI aims to study both conventional quantum Hall states and these newly discovered possibilities, known as topological band materials. The PI will investigate whether topological band materials can support states that have not been discovered before, even in traditional quantum Hall systems. A main goal of the research is to understand the properties of such states in an approximate analytical way where the underlying physics is clear. This will enable understanding the similarities and the differences between conventional quantum Hall states and those in topological band materials. The PI will also utilize this approach to investigate conventional quantum Hall materials subjected to elastic strain. Any real material contains lattice imperfections, substituted atoms, and defects, collectively known as disorder. The PI will develop a controlled approach to investigate the role of disorder where experiments on some quantum Hall states suggest that the effect of disorder is important.The PI will also contribute to the organization of Winter Schools in India and will participate in the reorganization of the University Honors Program which provides a mechanism for students to learn about many disciplines and benefit from experimental learning.TECHNICAL SUMMARYThis award supports theoretical research and education aimed to investigate quantum Hall states and topological states in materials. It has recently been established that materials with strong spin-orbit coupling can form new types of insulators, known as topological insulators, because of the topological properties of the band structure. When such bands are full, they have a quantized Hall conductance. With partial filling and strong electron-electron interactions fractional quantum Hall-like states form. The research has two major thrusts: 1. Investigating novel states in fractionally filled topological bands: The PI will use an analytical approach to investigate Composite Fermion states in topological bands. (a) Ground state energies for gapped states at the principal fractions and collective excitations will be computed in the Hamiltonian approach developed for the fractional quantum Hall effect. (b) Transitions between principal fraction states of different spin will be investigated using ground state energy crossings. (c) Two different possibilities for the half-filled state, an electron fluid and a Composite Fermion fluid, will be investigated. The nature of the phase transition and low-energy excitations near the phase transition will be studied. (d) Edge states of fractionally filled topological bands will be studied using a conserving approximation. This is relevant for determining whether the topological band materials have excitations other than those of conventional fractional quantum Hall states. (e) Two time-reversed copies of topological bands are a model of a time-reversal invariant topological insulator. Fractionally filled states of strongly interacting electrons will be studied in this model. (f) Tilted fields or strain in the conventional fractional quantum Hall effects produces an anisotropy which has been measured. The PI will develop an analytical theory of such anisotopic states, and potential phase transitions into nematic-like states. 2. Elucidating the role of quenched disorder in quantum Hall ferromagnets: The prototypical system is the filling 1 bilayer, where experimental observations pose numerous challenges to theory, and where disorder seems to be essential. (a) The PI and collaborators will, at the first stage, mimic the nonperturbative effects of disorder by imposing a strong periodic potential on the quantum Hall system. Hartree-Fock and effective low-energy theories will be used to determine the generation of topological charges in response to the potential. (b) Collective excitations will be computed to derive an experimental signature in light scattering of such states. (c) A low-energy field theory will be constructed near the phase transitions between different arrangements of topological charge. (d) Weak disorder will be put in at this stage and renormalization group techniques will be used to determine the low-energy long-wavelength behavior near the transitions. The PI will also contribute to the organization of Winter Schools in India and will participate in the reorganization of the University Honors Program which provides a mechanism for students to learn about many disciplines and benefit from experimental learning.

非技术摘要这一奖项支持理论研究和教育，旨在调查新的电子状态。通常认为电子是不可分割的，在室温和固态设备通常运行的条件下是正确的。这项研究最重要的是量子大厅状态，这些状态发生在二维电子中，通常是在半导体之间的人工设计的界面上，冷却至从绝对零的温度不到一个程度，并将其放置在垂直于底片的非常强的磁场中。在最简单的状态下，可以将电子视为“拆分”成三个称为复合费米子的对象。每个复合效率的电荷与其他外来性质的电荷是电子的三分之一。激发的电荷和其他属性取决于特定状态。其中一些状态提供了量子计算的可能平台。常规的半导体量子厅状态需要极端条件。在过去的十年中，已经提出了一种新的潜在实现这种状态的方法，其中某些材料内部的环境可以产生相当于非常强大的内部磁场。 PI旨在研究常规量子厅状态和这些新发现的可能性，称为拓扑结构材料。 PI将调查拓扑结构材料是否可以支持以前未发现的状态，即使在传统的量子厅系统中也是如此。该研究的一个主要目标是以近似分析的方式来了解这种状态的特性，在该方式中，基础物理学很明显。这将使常规量子厅状态与拓扑带材料中的相似性和差异。 PI还将利用这种方法来研究受弹性应变的常规量子厅材料。任何实际材料都包含晶格缺陷，取代原子和缺陷，统称为疾病。 PI将开发一种受控的方法来调查疾病的作用，在某些量子厅的实验表明，疾病的效果很重要。PI还将为印度冬季学校的组织组织做出贡献，并将参与大学荣誉计划的重组，该计划为学生提供了许多学科和受益的量化量级的材料，并授予了众多材料，并提供了旨在的材料。最近已经确定，由于带结构的拓扑特性，具有强旋转轨道耦合的材料可以形成新型的绝缘体（称为拓扑绝缘子）。当这样的乐队满足时，它们会有量化的大厅电导。局部填充和强烈的电子电子相互作用分数量子厅状状态形式。这项研究有两个主要的推力：1。在填充的拓扑谱带中研究新的状态：PI将使用分析方法研究拓扑谱带中的复合费米态。 （a）在主要分数和集体激励处的基态能量将在针对分数量子霍尔效应开发的汉密尔顿方法中计算。 （b）将使用基态能量交叉点研究不同自旋的主要分数状态之间的过渡。 （c）将研究半填充状态的两种不同的可能性，一种电子液和复合费用流体。将研究相变的相变和低能激发的性质。 （d）将使用保存近似研究对填充拓扑带的边缘状态进行研究。这与确定拓扑结构材料是否具有激发量相关，而不是传统的分数量子厅态。 （e）拓扑带的两个时间转换的副本是时间反转拓扑绝缘子的模型。 在此模型中，将研究强烈相互作用电子的部分填充状态。 （f）常规分数量子大厅效应中的倾斜场或应变会产生已测量的各向异性。 PI将开发出这种异位状态的分析理论，并将潜在的相转变为列明状状态。 2。阐明淬火障碍在量子霍尔铁磁体中的作用：原型系统是填充1双层，实验观察对理论构成了许多挑战，而疾病似乎是必不可少的。 （a）在第一阶段，PI和合作者将通过对量子厅系统施加强大的周期性潜力来模仿疾病的非扰动作用。 Hartree-Fock和有效的低能理论将用于确定响应潜力的拓扑费用。 （b）将计算集体激励以在此类状态的光散射中得出实验特征。 （c）将在拓扑电荷不同排列之间的相变附近构建低能场理论。 （d）在此阶段将进行弱小的疾病，并将使用重新归一化的组技术来确定过渡附近的低能长波长行为。 PI还将为印度冬季学校的组织做出贡献，并将参加大学荣誉计划的重组，该计划为学生提供了一种了解许多学科并从实验学习中受益的机制。