RUI - Anisotropy in Correlated Electronic Systems in Quantum Hall Regime

技术概述：该奖项支持量子霍尔态强相关二维电子系统各向异性相的理论研究和教育。PI旨在阐明各种据称具有液晶秩序的中间相的起源和稳定性。虽然高迁移率GaAs/AlGaAs异质结构中的各向异性电子相在近十年前被实验发现，但它们的最终性质仍然难以捉摸。实验表明，各向异性只在约100 mK的临界温度以下出现，并且只在高朗道水平下观察到。缺乏理解的各向异性电子相的一个关键方面是这些相相对于主体砷化镓晶格的晶轴的一致取向。PI认为磁输运各向异性的出现是电子形成具有液晶秩序的新电子相的标志。PI的目的是调查悬而未决的基本问题，包括：(i)各向异性的微观起源；（ii）垂直磁场中高朗道能级液晶态的性质；(3)各向异性液晶相在高朗道水平下稳定的物理机制；（iv）各向异性电子-电子扰动对各向异性相定向和稳定的作用；(v)在低温条件下，由弱基质介导的各向异性电子-电子摄动和倾斜磁场共同作用稳定的最低朗道能级存在各向异性液晶相。将进行数值和量子蒙特卡罗计算，以解决量子霍尔体系中有关各向异性的突出问题。该研究将有助于从理论上更好地理解低维强相关电子系统中的量子相变和各种新型液晶或混合相。本科生将能够参与有价值的研究经验。该奖项将进一步帮助加强研究和教育基础设施，为少数族裔HBCU机构中代表性不足的少数族裔学生提供帮助。通过一项外展活动，PI旨在培养贫困的当地社区和当地高中在K-12阶段对科学相关领域的兴趣。非技术概述：该奖项支持理论研究和教育，旨在了解电子在高磁场中被限制在一个平面内所表现出的物质的新状态。由半导体材料制成的巧妙设计的结构可以在二维空间中容纳电子。PI将使用先进的计算机模拟和理论方法来阐明当放置在高磁场中时这些结构中的电子的量子力学状态。与原子气体甚至铜线中的电子不同，这些状态下的电子以一种由量子力学精心设计的合作方式表现。PI试图研究一些有趣的状态，这些状态被认为类似于长分子的相，这些相具有特定的方向感，并且与液晶显示器中的相有关。PI表明，这些类似液晶的电子状态可以在实验尚未探索的特定情况下出现。从基础科学的角度来看，物质的新电子状态很有趣，但也是电子设备、传感器、计算等未来技术的潜在构建块。本科生将能够参与有价值的研究经验。该奖项将进一步帮助加强研究和教育基础设施，为少数族裔HBCU机构中代表性不足的少数族裔学生提供帮助。通过一项外展活动，PI旨在培养贫困的当地社区和当地高中在K-12阶段对科学相关领域的兴趣。

TECHNICAL SUMMARY:This award supports theoretical research and education on anisotropic phases of strongly correlated two-dimensional electronic systems in quantum Hall states. The PI aims to elucidate the origin and the stabilization of various intermediate phases purported to have liquid crystalline order. Though anisotropic electronic phases in high mobility GaAs/AlGaAs hetero-structures were discovered experimentally nearly ten years ago, their ultimate nature remains elusive. Experiments show anisotropy arises only below a critical temperature of about 100 mK and is observed only in high Landau levels. A key aspect of anisotropic electronic phases that lacks understanding is the consistent orientation of such phases with respect to the crystalline axes of the host GaAs crystal lattice.The PI takes the view that the emergence of magneto-transport anisotropy is an indicator that electrons have formed a novel electronic phase with liquid crystalline order. The PI aims to investigate outstanding fundamental issues, including: (i) the microscopic origin of anisotropy; (ii) the nature of liquid crystalline states in high Landau levels in perpendicular magnetic field; (iii) the physical mechanism of stabilization of anisotropic liquid crystalline phases in high Landau levels; (iv) the role played by an anisotropic electron-electron perturbation to orient and stabilize various anisotropic phases; and (v) the existence of anisotropic liquid crystalline phases in the lowest Landau level at low temperature stabilized by the combined effect of a weak substrate-mediated anisotropic electron-electron perturbation and a tilted magnetic field. Numerical and quantum Monte Carlo calculations will be performed to address outstanding questions about anisotropy in the quantum Hall regime. The research will contribute to a better theoretical understanding of quantum phase transitions and various novel liquid crystalline or hybrid phases in strongly correlated electronic systems in low dimensions. Undergraduate students will be able to participate in valuable research experiences. This award will further help to enhance research and education infrastructure for underrepresented minority students at a minority HBCU institution. Through an outreach activity, the PI aims to develop interest in science related areas at the K-12 level in underprivileged local communities and local high schools. NON-TECHNICAL SUMMARY:This award supports theoretical research and education with an aim to understand new states of matter exhibited by electrons in high magnetic fields and confined to a plane. Cleverly engineered structures made of semiconductor materials can hold electrons in two dimensions. The PI will use advanced computer simulation and theoretical methods to elucidate the quantum mechanical state of electrons in these structures when placed in a high magnetic field. Unlike gases of atoms or even electrons in a copper wire, electrons in these states behave in a cooperative way that is choreographed by quantum mechanics. The PI seeks to investigate intriguing states that are believed to be analogous to phases of long molecules -- phases that have the sense of a particular direction and are related to the ones in a liquid crystal display. The PI suggests that these liquid crystal like states of electrons can appear under specific circumstances not yet explored by experiments. New electronic states of matter are interesting from the perspective of fundamental science, but are also potential building blocks of future technologies for electronic devices, sensors, computation, and more. Undergraduate students will be able to participate in valuable research experiences. This award will further help to enhance research and education infrastructure for underrepresented minority students at a minority HBCU institution. Through an outreach activity, the PI aims to develop interest in science related areas at the K-12 level in underprivileged local communities and local high schools.