Exotic Quantum Liquid Phases Due to Intrinsic Degrees of Anisotropy

非技术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以及教育，包括研究电子被限制在两个维度，并受到相互作用和晶体环境的影响，导致首选方向。原子和分子由电子、质子和中子等基本粒子组成。电子通常与它们的原子紧密结合。材料是由数十亿个原子组成的，在金属和半导体材料中，一些电子可以相对自由地运动。这些电子可以像液体一样工作，很容易对外加电场、磁场和外加压力作出反应。例如，铜线在外加电场的作用下导电。由于材料的许多有趣的性质是由这种自由电子的行为决定的，因此研究电子物质在大电子系统中可能存在的状态的性质以及它们的性质与外部参数(如温度、电子密度和外加磁场)的关系是很自然的。PI将研究材料中的电子态，在这些材料中，自由电子被限制在二维空间，其中电子之间的相互作用和量子效应可能结合在一起，导致新的现象和新的物质电子态。如果相互作用不是很强，电子可能处于均匀的物质液体状态。这种液态的性质是各向同性的--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与方向有关。原子晶格的存在使电子的行为就像它们有一个有效质量，这取决于它们的运动方向。这可能会导致电子的行为像细长棒的液体一样，导致类似于液晶显示器中棒状分子所呈现的电子态。PI将研究由于各向异性而可能出现的电子态。这包括外部诱导的各向异性，例如在垂直于电子的2D世界施加强磁场时可能出现的各向异性状态。对新的电子状态的研究增加了导致新的电子设备技术的知识基础。该项目开展的研究活动将在HBCU的背景下为经济困难的学生提供研究机会，将加强本科生环境中的研究和教育，并将改善本科生对研究生学习的准备。总体而言，该项目将有助于加强当地机构的研究和教育基础设施，并导致代表不足的群体更广泛地参与科学。技术总结材料研究部和人力资源开发部为该奖项提供资金。它为研究强关联费米系统中新的各向异性奇异量子液相的出现提供了基础的理论和计算研究。PI将研究量子霍尔区中的二维电子系统，以及存在一定内部各向异性的具有变形费米表面的二维费米液相。PI的目的是了解各向异性电子有序态是如何在不同的量子相中产生的，以响应系统的本征各向异性。PI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，以及由各向异性有效质量和电子之间的各向异性相互作用势共同驱动的具有变形费米面的各向异性费米液相。这些理论方法可以应用于具有强质量各向异性的二维电子系统的实验，其中预计量子霍尔区将发生异常的各向异性输运。这项研究的思路可能对理解限制在砷化铝量子阱和相关系统中的二维电子系统的实验有一定的意义。在这些系统中，电子的有效质量各向异性比几乎可以是一个数量级。特别令人感兴趣的是，如何调整压电特性对各向异性有效电子相互作用的影响，以及由此产生的实验可观察的结果。可以提出实验来检测由于不同各向异性来源的相互作用而导致的传输特性中的特征。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相结合的方法，包括精确对角化和量子蒙特卡罗，来开展这项研究。学生将使用适合他们技能的方法，例如量子理论中的变分或微扰方法，或计算机模拟，以适当地增强他们的教育经验。这项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中领导职业。这个项目将通过加强管道，帮助少数族裔和经济困难的学生更多地参与科学和工程。这个奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.