RUI - Anisotropy in Correlated Electronic Systems in Quantum Hall Regime

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旨在阐明声称具有液晶顺序的各种中间相的起源和稳定性。虽然高迁移率GaAs/AlGaAs异质结中的各向异性电子相在近十年前就被实验发现，但其最终性质仍然难以理解。实验表明，各向异性只出现在低于约100 mK的临界温度，并观察到只有在高朗道水平。各向异性电子相的一个关键方面是缺乏理解的是相对于宿主GaAs晶格的晶轴，这些相的一致取向。PI认为，磁输运各向异性的出现是电子已经形成具有液晶顺序的新型电子相的指示器。该PI旨在研究突出的基本问题，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;（iii）高朗道能级各向异性液晶相稳定化的物理机制;（iv）各向异性电子-电子微扰对取向和稳定各种各向异性相所起的作用;（iv）各向异性电子-电子微扰对取向和稳定各种各向异性相所起的作用。以及（v）在低温下在最低朗道能级中存在各向异性液晶相，该液晶相通过弱的衬底介导的各向异性电子-电子扰动和倾斜磁场的组合效应而稳定。将进行数值和量子蒙特卡罗计算，以解决有关量子霍尔制度各向异性的突出问题。该研究将有助于更好地从理论上理解低维强关联电子系统中的量子相变和各种新型液晶或混合相。本科生将能够参与宝贵的研究经验。该奖项将进一步帮助加强研究和教育基础设施，为少数民族学生在少数民族HBCU机构。通过推广活动，PI的目的是在贫困的地方社区和当地高中培养K-12水平的科学相关领域的兴趣。非技术性总结：该奖项支持理论研究和教育，旨在了解电子在高磁场中表现出的新物质状态，并限制在平面上。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这些结构中电子在高磁场中的量子力学状态。与原子气体甚至铜线中的电子不同，处于这些状态的电子以量子力学设计的合作方式行为。PI试图研究被认为类似于长分子相的有趣状态-具有特定方向感并与液晶显示器中的相相关的相。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。 本科生将能够参与宝贵的研究经验。该奖项将进一步帮助加强研究和教育基础设施，为少数民族学生在少数民族HBCU机构。通过推广活动，PI的目的是在贫困的地方社区和当地高中培养K-12水平的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.