Theory of Novel Excitations in the Fractional Quantum Hall Effect

分数量子霍尔效应中的新激发理论

• 批准号: 1005536
• 负责人: Jainendra Jain
• 金额: $ 30万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005536&HistoricalAwards=false
• 关键词: Theory; Novel; Excitations; Fractional; Quantum

TECHNICAL SUMMARY This award supports theoretical research on the excitations of the fractional quantum Hall effect state. While definite progress has been made toward clarifying the physics of some of the excitations of the fractional quantum Hall effect state, many important issues remain unexplored. Employing a combination of numerical tools, such as exact diagonalization and quantum Monte Carlo techniques, and analytical approaches, including effective Chern Simons field theory, bosonization, and conformal field theory, the PI aims to address the following questions:(1) Does the fractional quantum Hall effect spectrum contain new magneto-roton collective modes at higher energies? If so, how will they manifest in inelastic light scattering or optical absorption experiments?(2) Do composite fermions generically form pairs in the lowest Landau level, and if so, how can they be observed?(3) How does an externally injected electron couple into high energy excitations of the fractional quantum Hall state? How many higher Landau-like levels of composite fermions are real? What is the nature of the neutral and charged excitations in higher electronic Landau levels? How does the spin degree of freedom alter the nature of excitations? (4) How are the fractional quantum Hall effect excitations affected by an anisotropy in the interaction?(5) What is the microscopic description of the edge excitations of more complex states, such as 2/5, and how does it compare to the predictions of the effective theory?The PI will work closely with experimental groups. The graduate students supported by this grant will receive a broad training ranging from massively parallel numerical computations to semiconductor physics to quantum field theory. The PI and his student will also devote a portion of their time in conveying the excitement of various physical phenomena and concepts in two dimensions to school students at all levels, with hands-on activities including various possible crystal structures in two dimensions, two dimensional models of gravity, and interference of waves in two dimensions. These will be combined to form an educational module entitled "Fun with Physics in Flatland", to be incorporated into existing educational and outreach programs at Penn State. NON-TECHNICAL SUMMARY This award supports theoretical study of collective quantum states of matter known as the fractional quantum Hall effect. These emerge when electrons confined to two dimensions are exposed to a strong magnetic field. This study will focus on excited states and their energies which are largely unexplored. Experimental efforts are beginning to investigate these excited states in hitherto inaccessible regimes. In this context, the PI's research is poised to make timely contributions to the interpretation of experiments. Employing a combination of numerical and analytical tools, the PI aims to investigate specific theoretical questions; some are related to predictions of new electronic states of matter in quantum Hall systems that might form the basis for a new high performance computer that exploits the manipulation of quantum mechanical states for its operation.During the course of this research, the PI will work closely with experimental groups. Graduate students supported by this award will receive a broad training ranging from computation to advanced analytical theoretical methods. The PI and his student will also devote a portion of their time in conveying the excitement of various physical phenomena and concepts in two dimensions to school students at all levels, with hands-on activities including various possible crystal structures in two dimensions, two dimensional models of gravity, and interference of waves in two dimensions. These will be combined to form an educational module entitled "Fun with Physics in Flatland", to be incorporated into existing educational and outreach programs at Penn State.

该奖项支持分数量子霍尔效应态激发的理论研究。虽然在澄清分数量子霍尔效应态的某些激发的物理学方面已经取得了明确的进展，但许多重要的问题仍未得到探索。采用精确对角化和量子蒙特卡罗技术等数值工具和分析方法，包括有效的Chern Simons场理论、玻色子化和共形场理论，PI旨在解决以下问题：(1)分数量子霍尔效应谱是否包含更高能量的新磁-转子集体模式？如果是这样，它们将如何在非弹性光散射或光吸收实验中表现出来？(2)复合费米子一般在最低朗道能级形成对吗？如果是，如何观测到它们？(3)外部注入的电子如何耦合到分数量子霍尔态的高能激发中？复合费米子有多少更高的类朗道能级是真实存在的？在较高电子朗道能级中，中性和带电激励的性质是什么？自旋自由度如何改变激发态的性质？(4)相互作用中的各向异性如何影响分数量子霍尔效应激发？(5)更复杂状态（如2/5）的边缘激发的微观描述是什么？它与有效理论的预测相比如何？PI将与实验组密切合作。该基金资助的研究生将接受从大规模并行数值计算到半导体物理到量子场论的广泛培训。PI和他的学生还将花一部分时间向各级学生传达二维中各种物理现象和概念的兴奋，包括各种可能的二维晶体结构，二维重力模型，以及二维波的干涉。这些课程将被整合成一个名为“Flatland with Physics in Fun”的教育模块，并被纳入宾夕法尼亚州立大学现有的教育和推广项目中。该奖项支持被称为分数量子霍尔效应的物质集体量子态的理论研究。当局限于二维空间的电子暴露在强磁场中时，就会出现这种现象。这项研究将集中在激发态及其能量上，这在很大程度上是未知的。实验工作已经开始在迄今为止无法进入的体制中研究这些激发态。在这种背景下，PI的研究准备对实验的解释做出及时的贡献。采用数值和分析工具的组合，PI旨在调查具体的理论问题；其中一些与量子霍尔系统中物质的新电子状态的预测有关，这可能成为利用量子力学状态操纵其运行的新型高性能计算机的基础。在这项研究的过程中，PI将与实验组密切合作。该奖项支持的研究生将接受从计算到高级分析理论方法的广泛培训。PI和他的学生还将花一部分时间向各级学生传达二维中各种物理现象和概念的兴奋，包括各种可能的二维晶体结构，二维重力模型，以及二维波的干涉。这些课程将被整合成一个名为“Flatland with Physics in Fun”的教育模块，并被纳入宾夕法尼亚州立大学现有的教育和推广项目中。