Exotic Quantum Liquid Phases Due to Intrinsic Degrees of Anisotropy

非技术性总结材料研究部和人力资源开发部为该奖项提供资金。它支持基础理论和计算研究和教育，包括研究局限于二维空间的电子，并受相互作用和导致优选方向的晶体环境的影响。原子和分子由电子，质子和中子等基本粒子组成。电子常常与其原子紧密结合。材料由数十亿个原子组成，在金属和半导体材料中，一些电子可以相对自由地移动。这些电子可以表现得像液体一样，并且可以很容易地响应外部施加的场，例如电场，磁场和施加的压力。由于材料的许多有趣的性质都是由这些自由电子的行为决定的，因此研究大型电子系统中电子物质的可能状态的性质以及它们的性质对外部参数（如温度、电子密度和外加磁场）的依赖性是很自然的。PI将研究材料中的电子状态，其中自由电子被限制在二维空间，电子和量子效应之间的相互作用可能会联合收割机导致新的现象和新的物质电子状态。如果相互作用不是很强，电子可能处于均匀的液态物质中。这种液体状态的性质将是各向同性的-在所有方向上都是一样的。然而，电子之间的有效相互作用可能是各向异性的或方向相关的。原子晶格的存在使得电子的行为就好像它们有一个取决于它们运动方向的有效质量。这可能导致电子表现得像细长杆的液体，从而导致与液晶显示器中的杆状分子所呈现的电子状态类似的电子状态。PI将研究可能由于各向异性而产生的电子状态。这包括外部诱导的各向异性，例如在垂直于电子的2D世界的强磁场的应用下可能出现的各向异性状态。对新电子状态的研究增加了导致新电子设备技术的知识基础。在这个项目中进行的研究活动将导致在HBCU的设置经济困难的学生的研究机会，将加强在本科环境中的研究和教育，并将提高本科生的研究生学习的准备。总的来说，该项目将有助于加强当地机构的研究和教育基础设施，并导致更广泛地参与科学中代表性不足的群体。技术摘要材料研究部和人力资源开发部为该奖项提供资金。它支持的基础理论和计算研究，调查出现的新的各向异性奇异量子液相在强关联费米系统。PI将研究量子霍尔制度中的二维电子系统和存在某种内部各向异性程度的变形费米表面的二维费米液相。PI旨在了解各向异性电子有序态如何在各种量子相中出现，以响应系统的固有各向异性。该项目还将研究新的奇异各向异性相的性质，例如由各向异性相互作用势驱动的各向异性量子霍尔液相和由各向异性有效质量和电子之间的各向异性相互作用势驱动的具有变形费米表面的各向异性费米液相。三维电子系统具有很强的质量各向异性，在量子霍尔制度不寻常的各向异性运输预计。这项研究的想法可以相关的理解实验中的二维系统的电子限制在砷化铝量子威尔斯和相关的系统。在这些系统中，电子有效质量各向异性比几乎可以是一个数量级。特别感兴趣的是如何调整压电性能的影响各向异性的有效电子相互作用，以及由此产生的实验观察到的后果。 可以提出实验来检测由不同各向异性源的相互作用引起的输运性质中的特征。PI还将考虑其他物理系统，包括各向异性晶格陷阱中的超冷原子。PI和他的团队将使用理论和计算方法的结合，包括精确对角化和量子蒙特卡罗，来进行研究。学生将使用适合他们技能的方法，如量子理论的变分或微扰方法，或计算机模拟，以提高他们的教育经验。该研究为教育和指导提供了一个环境，以提高人们对科学的兴趣，并在STEM领域引领职业生涯。该项目将通过加强管道帮助扩大少数民族和经济困难学生在科学和工程方面的参与。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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 and education involving the study of electrons confined to two dimensions and subject to interactions and crystal environments that lead to a preferred direction.Atoms and molecules are made of elementary particles such as electrons, protons, and neutrons. Electrons are often tightly bound to their atoms. Materials are made of many billions of atoms, and in metals and semiconductor materials some electrons can move relatively freely. These electrons can behave like a liquid and can easily respond to externally applied fields, such as electric fields, magnetic fields, and applied pressure. For example, a copper wire conducts electricity in response to an applied electric field.Since many interesting properties of materials are determined by the behavior of such free electrons, it is natural to study the nature of the possible states of electronic matter that arise in large systems of electrons and the dependence of their properties on external parameters, such as temperature, electron density, and applied magnetic field. The PI will study electronic states in materials where free electrons are restricted to two-dimensions where the interaction between electrons and quantum effects may combine leading to new phenomena and new electronic states of matter. The electrons may be in a uniform liquid state of matter if interactions are not very strong. The properties of such a liquid state would be isotropic - the same in all directions. However, it is possible that effective interactions between electrons are anisotropic or direction dependent. The presence of the crystalline lattice of atoms makes electrons behave as though they have an effective mass that can depend on the direction of their motion. This may lead to electrons behaving like a liquid of elongated rods leading to electronic states analogous to those assumed by the rod-like molecules in a liquid crystal display. The PI will investigate electronic states that may arise as a consequence of anisotropy. This includes externally induced anisotropy, such as the anisotropic states that could arise under the application of a strong magnetic field perpendicular to the 2D world of the electrons. The investigation of new electronic states adds to the intellectual foundations that lead to new electronic device technologies. The research activities conducted in this project will lead to research opportunities for economically challenged students in the setting of a HBCU, will enhance research and education in an undergraduate environment, and will improve the preparation of undergraduate students for graduate studies. Overall, this project will help to enhance the research and the education infrastructure at the local institution, and lead to broader participation of underrepresented groups in science.TECHNICAL SUMMARYThe Division of Materials Research and the Division of Human Resource Development contribute funds to this award. It supports fundamental theoretical and computational research to investigate the emergence of novel anisotropic exotic quantum liquid phases in strongly correlated Fermi systems. The PI will study two-dimensional systems of electrons in the quantum Hall regime and two-dimensional Fermi liquid phases with deformed Fermi surfaces in presence of some internal degree of anisotropy. The PI aims to understand how anisotropic electronic ordered states arise in various quantum phases in response to intrinsic anisotropy of the system. The PI will also investigate the nature of novel exotic anisotropic phases such as anisotropic quantum Hall liquid phases driven by an anisotropic interaction potential and anisotropic Fermi liquid phases with deformed Fermi surfaces driven by a combination of anisotropic effective mass and an anisotropic interaction potential between electrons.The theoretical approaches can be applied to experiments on two-dimensional electron systems with strong mass anisotropy where unusual anisotropic transport in the quantum Hall regime is anticipated. The ideas of this research can be relevant to understand experiments in two-dimensional systems of electrons confined in aluminum arsenide quantum wells and related systems. The electron effective mass anisotropy ratios can be almost one order of magnitude in these systems. Of particular interest is how tuning piezoelectric properties effects the anisotropic effective electron interactions, and the resulting experimentally observable consequences. Experiments may be proposed to detect signatures in transport properties resulting from the interplay of different sources of anisotropy. The PI will consider other physical systems as well, including ultracold atoms in anisotropic lattice traps. The PI and his team will use a combination of theoretical and computational methods, including exact diagonalization and quantum Monte Carlo, to carry out the research. Students will use methods suited to their skills, such as variational or perturbation methods from quantum theory, or computer simulations, in order to enhance their educational experience as appropriate. The research provides a setting for education and mentoring to enhance interest in science and leading careers in STEM. This project will help broaden participation of minority and economically challenged students in science and engineering through enhancing the pipeline.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.