RUI: Theoretical (Numerical) Investigations of Novel Transport and Topological Properties of Two-Dimensional Interacting Electron Systems

RUI：二维相互作用电子系统新输运和拓扑性质的理论（数值）研究

• 批准号: 0605696
• 负责人: Donna Sheng
• 金额: $ 10.5万
• 依托单位: The University Corporation, Northridge
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605696&HistoricalAwards=false
• 关键词: RUI; Theoretical; Numerical; Investigations; Novel

This project involves theoretical (numerical) approaches to the fundamental nature of new emerging quantum phases and associated novel transport and topological properties in several electron systems. The research will be done at a predominantly undergraduate institution and will afford opportunities for undergraduates and graduate students to participate in the research. The research is comprised of three projects.Firstly, the Principal Investigator (PI) proposes to study the new emerging quantum Hall effect (QHE) in coupled bi-layer electron systems with strong electron-electron interaction. A new quantum phase characterized by the coexistence of integer QHE and exciton condensation has recently been established experimentally, by conducting counter-flow currents in bi-layer systems. Novel fractional QHE states including the non-Abelian paired Hall states are also suggested by experiments. On the theoretical side, it remains an open issue how to characterize quantum Hall states with features besides their charge (total) Hall conductance. A new numerical method based on a matrix of topological invariant Chern numbers has been developed by the PI and her collaborators for this purpose, which will be applied to study the Coulomb drag transport, charge Hall effect and the transport properties in counter-flow current measurement as well as quantum phase transitions in bi-layer systems. We are aiming at understanding the existing experimental observations, characterizing the nature of quantum phase transitions for these new quantum states, and making quantitative predictions regarding transport measurements for future experiments.Secondly, the PI proposes to study the novel QHE of two-dimensional (2D) interacting Dirac fermions in graphene. In recent experiments, a series of QHE plateaus with unconventional quantization rule have been observed for Dirac fermions in single-atom-thick graphite (graphene) system. So far, the interplay of the novel band structure, disorder potential and Coulomb interaction has not been studied yet, which may soon become one of the central topics in the field of QHE. We propose to perform a systematic numerical study using microscopic band model taking into account all these important aspects of the material, which may provide valuable information and further stimulate experimental research.Thirdly, the fundamental problem whether electron-electron interaction can lead to spin-liquid state with topological ordering and fractionalization in 2D electron system will also be investigated numerically. Understanding this issue will have important impact on the theory of strongly correlated electron systems and the future development of the topological quantum computing. We are aiming to identify some concrete examples of topological ordered spin-liquid state in 2D electron systems based on extensive numerical calculations of low energy spectrum, topological degeneracy and spin-spin correlation function.The intellectual merit of this proposal is that the topics addressed are of fundamental importance for the understanding of the new physical phenomena in 2D electron systems. The broader impact on society of the proposed research project is twofold. Firstly, the project will impact on the future development of new magneto-electronic devices and topological quantum computing qubits. Secondly, the present project will provide students and postdoctoral fellows with excellent introduction and training about how to carry out research at the forefront of physics and will also prepare them for dealing with practical problems in future academic and non-academic careers. In the past a few years, PI and her collaborators have developed novel and effective numerical methods, based on topological invariant quantities, to study the quantum transport and topological properties of interacting electron systems. Thus we believe that the proposed research can be carried out effectively and successfully.Non-Technical Abstract: This project involves theoretical (numerical) approaches to the fundamental nature of new emerging quantum phases and associated novel transport and topological properties in several electron systems that are found in solids. The research will be done at a predominantly undergraduate institution and will afford opportunities for undergraduates and graduate students to participate in the research.

该项目涉及对新出现的量子相的基本性质以及几个电子系统中相关的新颖输运和拓扑特性的理论（数值）方法。该研究将在以本科生为主的机构中进行，并将为本科生和研究生提供参与研究的机会。 该研究由三个项目组成。首先，首席研究员（PI）提出研究具有强电子-电子相互作用的耦合双层电子系统中新兴的量子霍尔效应（QHE）。最近通过在双层系统中传导逆流电流，通过实验建立了一种以整数 QHE 和激子凝聚共存为特征的新量子相。实验还提出了新的分数 QHE 态，包括非阿贝尔配对霍尔态。在理论方面，如何用电荷（总）霍尔电导之外的特征来表征量子霍尔态仍然是一个悬而未决的问题。为此，PI及其合作者开发了一种基于拓扑不变陈数矩阵的新数值方法，该方法将用于研究库仑阻力输运、电荷霍尔效应和逆流电流测量中的输运特性以及双层系统中的量子相变。我们的目标是了解现有的实验观察结果，表征这些新量子态的量子相变的本质，并对未来实验的输运测量做出定量预测。其次，PI建议研究二维（2D）的新型QHE ）石墨烯中狄拉克费米子的相互作用。最近的实验中，在单原子厚度的石墨（石墨烯）系统中观察到狄拉克费米子一系列具有非常规量子化规则的QHE平台。到目前为止，新型能带结构、无序势和库仑相互作用之间的相互作用尚未得到研究，这可能很快成为QHE领域的中心课题之一。我们建议利用微观能带模型进行系统的数值研究，考虑到材料的所有这些重要方面，这可能会提供有价值的信息并进一步激发实验研究。第三，电子-电子相互作用是否可以导致自旋液体的根本问题二维电子系统中的拓扑有序和分级状态也将进行数值研究。理解这个问题将对强相关电子系统理论和拓扑量子计算的未来发展产生重要影响。我们的目标是基于低能谱、拓扑简并和自旋-自旋相关函数的广泛数值计算，确定二维电子系统中拓扑有序自旋-液态的一些具体例子。该提案的智力优点在于，所讨论的主题是对于理解二维电子系统中的新物理现象具有根本重要性。拟议的研究项目对社会的更广泛影响是双重的。首先，该项目将影响新型磁电子器件和拓扑量子计算量子位的未来发展。其次，本项目将为学生和博士后提供有关如何在物理学前沿开展研究的优秀介绍和培训，并为他们在未来学术和非学术职业中处理实际问题做好准备。在过去的几年中，PI 和她的合作者开发了基于拓扑不变量的新颖有效的数值方法，以研究相互作用电子系统的量子输运和拓扑性质。因此，我们相信所提出的研究可以有效且成功地进行。 非技术摘要：该项目涉及对新兴量子相的基本性质以及几个电子系统中相关的新颖输运和拓扑性质的理论（数值）方法存在于固体中。该研究将在以本科生为主的机构中进行，并将为本科生和研究生提供参与研究的机会。