RUI - Anisotropy in Correlated Electronic Systems in Quantum Hall Regime

技术综述：该奖项支持对量子霍尔态中强关联二维电子系统各向异性相的理论研究和教育。等电点旨在阐明各种据称具有液晶有序的中间相的起源和稳定性。尽管高迁移率的GaAs/AlGaAs异质结中的各向异性电子相在近十年前就已被实验发现，但它们的最终性质仍然难以捉摸。实验表明，只有在约100mK的临界温度以下才会出现各向异性，并且只有在高朗道能级才能观察到各向异性。各向异性电子相的一个关键问题是各向异性电子相相对于主晶格轴的取向一致。PI认为，磁输运各向异性的出现是电子形成具有液晶有序的新电子相的标志。PI旨在研究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Landau能级的液晶态的性质；(Iii)高Landau能级中各向异性液晶相稳定的物理机制；(Iv)各向异性电子微扰在定向和稳定各种各向异性相方面所起的作用；以及(V)低温下最低Landau能级中各向异性液晶相的存在，由弱衬底介导的各向异性电子-电子微扰和倾斜磁场的综合影响而稳定。将进行数值计算和量子蒙特卡罗计算，以解决有关量子霍尔区各向异性的悬而未决的问题。这一研究将有助于从理论上更好地理解低维强关联电子系统中的量子相变和各种新颖的液晶或杂化相。本科生将能够参与有价值的研究经验。这一奖项将进一步帮助加强HBCU一所少数族裔机构中代表不足的少数族裔学生的研究和教育基础设施。通过一项外展活动，该协会的目标是在贫困的当地社区和当地高中培养对K-12级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，目的是了解电子在强磁场中表现出的新的物质状态，并将其限制在平面上。由半导体材料制成的精心设计的结构可以在两个维度上容纳电子。PI将使用先进的计算机模拟和理论方法来阐明这些结构中电子在强磁场中的量子力学状态。与铜线中的原子气体甚至电子不同，处于这些状态的电子的行为方式是由量子力学精心设计的。PI试图研究被认为类似于长分子的相的有趣状态--具有特定方向并与液晶显示器中的相相关的相。等电点表明，这些类液晶态的电子可以在尚未被实验探索的特定环境中出现。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。这一奖项将进一步帮助加强HBCU一所少数族裔机构中代表不足的少数族裔学生的研究和教育基础设施。通过一项外展活动，该协会的目标是在贫困的当地社区和当地高中培养对K-12级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.