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Breakdown of Rotational Invariance in Quantum Hall Systems with Anisotropic Interaction

具有各向异性相互作用的量子霍尔系统中旋转不变性的分解

基本信息

批准号：
1705084
负责人：
Orion Ciftja
金额：
$ 20万
依托单位：
Prairie View A & M University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1705084&HistoricalAwards=false
关键词：
Breakdown Rotational Invariance Quantum Hall

项目摘要

NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Human Resource Development contribute funds to this award. It supports fundamental theoretical and computational research on two-dimensional systems of electrons that interact strongly with each other leading to novel electronic states that spontaneously develop a preferred direction. Two-dimensional systems of electrons can be created at the interface of two semiconductors, and they manifest intriguing properties in the presence of a strong perpendicular magnetic field. In that situation, electrons are predicted to form a liquid-like state of matter, exhibiting properties that appear the same in all directions, that is, they are isotropic. However, the presence of an anisotropic or direction-dependent interaction between electrons may drastically change the system's properties, resulting in quantum mechanical states of electrons that are analogous to the states of long molecules in liquid crystals, which form the basis of modern liquid-crystal displays. The PI and his team will use analytical and computational methods to understand the nature of the anisotropy in a system of electrons that interact with an anisotropic interaction potential. The research will contribute to the intellectual foundations that lead to new electronic and optical device technologies.Undergraduate, and often minority, students at the Historically Black Prairie View A & M University will be trained in applying analytical methods and in carrying out numerical simulations. The students will gain important research experience that can help them in their pursuit of future graduate studies, and will help enhance the research and education infrastructure of the institution. The PI will carry out outreach activities that aim to increase interest in science topics at local communities and high schools.TECHNICAL SUMMARYThis award supports theoretical research and education on the emergence of anisotropic orders in strongly correlated quantum Hall systems of electrons in the presence of an anisotropic interaction potential. An anisotropic interaction potential may naturally lead to anisotropic order at regimes where only an isotropic liquid was previously thought possible. These novel quantum phases may possess unconventional properties of great interest to the broad field of theoretical condensed matter physics.The project will develop a framework to understand the emergence of anisotropic order in quantum Hall systems in the presence of an anisotropic interaction potential in the extreme quantum limit. The research aims to explore outstanding issues such as: i) the stability of novel anisotropic quantum Hall liquid phases at odd-denominator filling factors of the lowest Landau level driven by an anisotropic Coulomb interaction potential between electrons, and ii) the stability of novel anisotropic Fermi liquid phases at even-denominator filling factors of the lowest Landau level driven by an anisotropic Coulomb interaction potential between electrons. The PI and his research team will use a combination of analytical and computational methods to carry out the research activities.Undergraduate, and often minority, students at the Historically Black Prairie View A & M University will be trained in applying analytical methods and in carrying out numerical simulations. The students will gain important research experience that can help them in their pursuit of future graduate studies, and will help enhance the research and education infrastructure of the institution. The PI will carry out outreach activities that aim to increase interest in science topics at local communities and high schools.

非技术性总结材料研究部和人力资源开发部为该奖项提供资金。它支持对电子的二维系统的基础理论和计算研究，这些系统彼此强烈相互作用，导致自发地发展出优选方向的新电子状态。二维电子系统可以在两个半导体的界面处产生，它们在强垂直磁场的存在下表现出有趣的特性。在这种情况下，电子被预测会形成类似液体的物质状态，表现出在所有方向上都相同的性质，也就是说，它们是各向同性的。然而，电子之间的各向异性或方向相关相互作用的存在可能会彻底改变系统的性质，导致电子的量子力学状态类似于液晶中长分子的状态，这构成了现代液晶显示器的基础。PI和他的团队将使用分析和计算方法来理解与各向异性相互作用势相互作用的电子系统中各向异性的性质。这项研究将有助于知识基础，导致新的电子和光学器件技术。本科生，往往是少数民族，学生在历史上黑草原视图A M大学将在应用分析方法和进行数值模拟培训。学生将获得重要的研究经验，可以帮助他们在未来的研究生学习的追求，并将有助于加强该机构的研究和教育基础设施。PI将开展旨在提高当地社区和高中对科学主题的兴趣的外展活动。技术总结该奖项支持在各向异性相互作用势存在的情况下，强相关量子霍尔电子系统中各向异性订单的出现的理论研究和教育。各向异性的相互作用势可以自然地导致各向异性秩序的制度，只有各向同性液体以前被认为是可能的。这些新的量子相可能具有非常规的性质，对理论凝聚态物理学的广泛领域具有极大的兴趣。该项目将开发一个框架，以理解在极端量子极限下存在各向异性相互作用势的量子霍尔系统中各向异性秩序的出现。本研究旨在探索两个突出问题：i）由电子间各向异性库仑相互作用势驱动的最低朗道能级奇分母填充因子下的新型各向异性量子霍尔液相的稳定性; ii）由电子间各向异性库仑相互作用势驱动的最低朗道能级偶分母填充因子下的新型各向异性费米液相的稳定性。PI和他的研究团队将使用分析和计算方法相结合来开展研究活动。历史上的黑草原视图A M大学的本科生，通常是少数民族学生，将接受应用分析方法和进行数值模拟的培训。学生将获得重要的研究经验，可以帮助他们在未来的研究生学习的追求，并将有助于加强该机构的研究和教育基础设施。PI将开展外联活动，旨在提高当地社区和高中对科学主题的兴趣。