Breakdown of Rotational Invariance in Quantum Hall Systems with Anisotropic Interaction

材料研究司和人力资源开发司为本奖项提供资金。它支持二维电子系统的基础理论和计算研究，这些电子系统相互作用强烈，导致新的电子状态自发地发展出一个优先方向。二维电子系统可以在两个半导体的界面上产生，并且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，预计电子会形成一种类似液体的物质状态，在所有方向上都表现出相同的性质，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依赖相互作用的存在可能会极大地改变系统的性质，导致电子的量子力学状态类似于液晶中的长分子状态，这是现代液晶显示的基础。PI和他的团队将使用分析和计算方法来了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本质。这项研究将为开发新的电子和光学器件技术奠定知识基础。历史黑人草原景观大学（historical Black Prairie View A & &; M University）的本科生，通常是少数族裔学生，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，有助他们日后继续深造，并有助加强香港大学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。该奖项支持在各向异性相互作用势存在的强相关量子霍尔系统中出现各向异性序的理论研究和教育。在以前认为只有各向同性液体可能存在的情况下，各向异性相互作用势自然会导致各向异性秩序。这些新的量子相可能具有对理论凝聚态物理的广泛领域具有极大兴趣的非常规性质。该项目将开发一个框架来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。本研究旨在探索在电子间各向异性库仑相互作用势驱动下新型各向异性量子霍尔液相在最低朗道能级奇分母填充因子下的稳定性，以及在电子间各向异性库仑相互作用势驱动下新型各向异性费米液相在最低朗道能级偶分母填充因子下的稳定性等突出问题。PI和他的研究团队将采用分析和计算相结合的方法来开展研究活动。历史黑人草原景观大学（historical Black Prairie View A & &; M University）的本科生，通常是少数族裔学生，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，有助他们日后继续深造，并有助加强香港大学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。

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.