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.

该项目涉及一些新兴量子阶段的基本性质以及在几种电子系统中相关的新型传输和拓扑特性的理论（数值）方法。这项研究将在一个主要的本科机构中进行，并为本科生和研究生参加研究的机会。 这项研究由三个项目组成。首先，首席研究员（PI）提议研究具有较强电子电子相互作用的耦合双层电子系统中新的新兴量子霍尔效应（QHE）。最近通过在双层系统中进行反流电流，通过实验建立了一个以整数QHE和激子冷凝的共存为特征的新量子相。实验也建议新的新型QHE国家在内，包括非亚伯配对的霍尔状态。从理论方面来说，它仍然是一个空旷的问题。为此目的，PI及其合作者开发了一种基于拓扑不变数矩阵的新数值方法，该方法将用于研究库仑阻力传输，充电厅效应，电荷霍尔效应和反流电流测量中的运输属性以及双层系统中的量子相变。我们旨在理解现有的实验观察结果，表征这些新量子状态的量子相变的性质，并对未来实验的运输测量进行定量预测。第二，PI提议研究二维（2d）相互作用的二维（2d）相互作用的dirac fermions的新颖QHE。在最近的实验中，已经观察到一系列具有非常规量化规则的QHE高原针对单原子石墨（石墨烯）系统中的狄拉克费米子。到目前为止，尚未研究新型带结构，无序潜力和库仑相互作用的相互作用，这可能很快成为QHE领域的中心主题之一。我们建议使用微观带模型进行系统的数值研究，以考虑材料的所有重要方面，这可能会提供有价值的信息并进一步刺激实验研究。三分之二的是，在2D电子系统中，还会在2D电子系统中进行拓扑液体的旋转状态和分数化，这是基本问题。了解此问题将对强相关的电子系统的理论以及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量谱，拓扑脱位和自旋旋转相关功能的广泛数值计算，确定2D电子系统中拓扑排序旋转状态的一些具体示例。该提议的智力优点是该提议的智力优点是，对新的物理局势的理解至关重要。对拟议研究项目的社会的更广泛影响是双重的。首先，该项目将影响新的磁电子设备和拓扑量子计算量子的未来开发。其次，本项目将为学生和博士后研究员提供出色的介绍和培训，介绍如何在物理学的最前沿进行研究，还将为在未来的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和她的合作者基于拓扑数量开发了新颖有效的数值方法，以研究相互作用电子系统的量子传输和拓扑特性。因此，我们认为拟议的研究可以有效，成功地进行。没有技术摘要：该项目涉及理论（数值）方法，用于在固体中发现的几个电子系统中新出现的量子阶段以及相关的新型量子和拓扑特性的基本性质。这项研究将在一个主要的本科机构中进行，并为本科生和研究生参加研究的机会。