RUI-Unconventional Anisotropic Order in Strongly Correlated Fermi Systems

非技术总结该奖项支持对电子系统的基本理论和计算研究，这些电子系统相互作用强烈，导致新的电子态自发地发展为首选方向。这些状态对外加磁场或电场的响应取决于磁场相对于首选方向的相对取向。PI将研究如何产生具有优先方向的态，即使两个电子之间的基本相互作用只取决于它们之间的距离，因此，对于任何方向都是相同的。特别令人感兴趣的是，在两个半导体的界面上，限制在平面上的电子如何出现各向异性状态，并暴露在垂直或近垂直的磁场中。PI将研究电子的量子力学状态，这种状态与液晶中长分子的状态相似，这构成了现代显示技术的基础。这项研究有助于为产生新的电子和光学设备技术奠定智力基础。这项研究项目提供了一个有效的工具，让本科生参与研究，并培训他们的技能，这些技能将在现代技术劳动力中具有价值。本科生，通常是少数民族学生，将参与这项研究的重要方面。由于研究将需要使用各种方法方法探索各种模型，本科生有许多机会获得重要的研究经验，这些经验可以帮助他们继续未来的研究生学习。该项目将有助于加强当地机构的研究和教育基础设施。通过外展活动，PI旨在提高当地社区和高中对科学主题的兴趣，最终有助于更广泛地参与科学。技术总结该奖项支持研究和教育，目的是调查在绝对零度下强关联费米子系统中非传统各向异性秩序的出现。在这种情况下，相互作用和量子效应之间的相互作用可能导致具有非常规性质的新型量子相的稳定。这个项目的主要目标是研究如何在具有非单调但各向同性相互作用势的强关联费米系统中稳定各种具有液晶有序的非传统各向异性相。本研究的一个重点是研究各向同性相互作用势如何触发各向异性行为。PI和他的研究团队将使用理论和计算方法来解决有关新型各向异性有序和相变的出现的悬而未决的问题，这些相变导致非常规有序的量子态。PI旨在通过探索从自发费米表面形变到磁场中新的各向异性液晶相的机制，来建立一个框架来理解各种相关费米子系统中各向异性有序的出现。PI的目的是促进对几个基本问题的理解，包括：(I)由于非单调相互作用势而导致的各向异性费米液相的稳定性，即各向同性相互作用势如何驱动相关的费米系统走向各向异性有序；(Ii)最近发现的倾斜磁场中类Laughlin填充因子的各向异性量子霍尔相的性质；以及(Iii)弱磁场中各向异性液晶相在弱各向异性扰动中的性质，这些扰动打破了主要相互作用势的旋转对称性。这项研究项目提供了一个有效的工具，让本科生参与研究并培训他们在现代技术劳动力中有价值的技能。本科生，通常是少数民族学生，将参与这项研究的重要方面。由于这项研究将需要使用各种方法探索各种模型，本科生有很多机会获得重要的研究经验，这些经验可以帮助他们继续未来的研究生学习。该项目将有助于加强当地机构的研究和教育基础设施。通过外展活动，PI旨在提高当地社区和高中对科学主题的兴趣，最终促进更广泛的科学参与。

NONTECHNICAL SUMMARYThis award supports fundamental theoretical and computational research on systems of electrons that interact strongly with each other leading to novel electronic states that spontaneously develop a preferred direction. How these states respond to say, an applied magnetic or electric field depends on the relative orientation of the field to the preferred direction. The PI will investigate how states with a preferred direction can arise eventhough the fundamental interaction between two electrons depends only on distance between them and so, is the same for any direction. Of particular interest is how anisotropic states emerge in electrons confined to a plane at the interface of two semiconductors and exposed to a perpendicular or nearly perpendicular magnetic field. The PI will investigate quantum mechanical states of electrons that are curiously analogous to the states of long molecules in liquid crystals that form the basis of modern display technology. This research contributes to the intellectual foundations that lead to new electronic and optical device technologies. This research project provides an effective vehicle for involving undergraduate students in research and training them in skills that will be valuable in the modern technical workforce. Undergraduate students, often minority students, will be involved in important aspects of this research. Because the research will require exploring a variety of models using various methods methods, there are many opportunities for undergraduate students to gain important research experience that can help them as they pursue future graduate studies. This project will help to enhance the research and the education infrastructure at the local institution. Through outreach activities, the PI aims to increase interest in science topics at local communities and high schools ultimately contributing to broader participation in science.TECHNICAL SUMMARYThis award supports research and education with the aim to investigate the emergence of unconventional anisotropic order in strongly correlated Fermion systems at absolute zero temperature. The interplay between interactions and quantum effects in this regime may lead to the stabilization of novel quantum phases with unconventional properties. The main goal of this project is to study how various unconventional anisotropic phases with liquid crystalline order can be stabilized in strongly correlated Fermi systems with non-monotonic but isotropic interaction potentials. A focus of this research is to investigate how isotropic interaction potentials trigger anisotropic behavior. The PI and his research team will employ theoretical and computational methods to address outstanding questions regarding the appearance of novel types of anisotropic ordering and phase transitions leading to unconventionally ordered quantum states. The PI aims to develop a framework to understand the emergence of anisotropic order in various correlated Fermion systems by exploring mechanisms ranging from spontaneous Fermi surface deformations to novel anisotropic liquid crystalline phases in a magnetic field. The PI aims to advance understanding of several fundamental issues including: (i) The stabilization of anisotropic Fermi liquid phases due to a non-monotonic interaction potential, namely, how isotropic interaction potentials can drive a correlated Fermi systems towards anisotropic order; (ii) The nature of the recently discovered anisotropic quantum Hall phases in tilted magnetic field for Laughlin-like filling factors in the first excited Landau level; and (iii) The nature of anisotropic liquid crystalline phases in a weak magnetic field in presence of weak anisotropic perturbations that break the rotational symmetry of the dominant interaction potential.This research project provides an effective vehicle for involving undergraduate students in research and training them in skills that will valuable in the modern technical workforce. Undergraduate students, often minority students, will be involved in important aspects of this research. Because the research will require exploring a variety of models using various methods, there are many opportunities for undergraduate students to gain important research experience that can help them as they pursue future graduate studies. This project will help to enhance the research and the education infrastructure at the local institution. Through outreach activities, the PI aims to increase interest in science topics at local communities and high schools ultimately contributing to broader participation in science.