CAREER:Topological and Strongly Correlated Electronic Phases

技术总结这个职业奖支持拓扑和强相关的物质电子相理论的研究和教育的综合计划。拓扑相是凝聚态物理学中一个新的、迅速扩展的前沿领域。 它们对缺陷和无序的鲁棒性使它们在某些应用中特别有前途。 PI建议使用分析和数值方法相结合，重点放在前者，研究三类相关的电子态物质：1。零温度和非零温度下的一维强相互作用系统。 特别强调的是高度热化的自旋自由度的制度。将研究所谓的自旋非相干Luttinger液体的各个方面。2.单层和多层分数量子霍尔系统中的有限尺寸效应。 实现非阿贝尔准粒子统计的相位将受到最多的关注，并将努力制定实验确定其存在的建议。3.量子液体和拓扑绝缘体。PI建议研究自旋-轨道耦合在实现和稳定不同类型的表现出拓扑秩序的物质中的作用。该提案的教育重点旨在促进发现，促进科学教学，扩大代表性不足群体的参与，并向更广泛的公众宣传科学在我们社会福祉中发挥的核心作用。 这些目标将通过多种方式实现。其中包括：+与高中生，特别是那些历史上代表性不足的群体的学生进行外联。PI将访问当地奥斯汀地区拥有大量西班牙裔/拉丁裔人口的高中，与学生和教师互动。指导女科学家。PI将参加德克萨斯大学为对物理感兴趣的有才华的女高中生举办的“爱丽丝梦游仙境”暑期项目。增加德克萨斯州K-12科学教师的数量。 PI积极参与招收本科生到科学教育专业。本科生参与研究。PI将监督本科生，因为他们追求的研究，为他们提供一个有意义的生活品味作为一个科学家。与奥斯汀当地的高科技产业合作。PI将通过与私营部门的科学家合作加强与私营部门的联系。在得克萨斯州自然科学中心与更广泛的公众接触。 PI计划举办公开讲座，以令人兴奋和信息丰富的方式展示研究成果。非技术总结该职业奖支持新物质状态理论的研究和教育综合计划。原子在不同的材料中以截然不同的方式组织自己。金刚石中的碳原子与石墨中的碳原子自我排列不同，从而产生明显不同的性质。精确的对称性数学概念基于晶体如何翻转、旋转或移动以使晶体看起来相同，从而能够对相位进行分类。这种分类足够普遍，可以涵盖由原子组成的晶体，以及材料中电子的相，例如磁性或量子力学状态，其中电子本身组织成晶体。对被困在平面内并暴露在强磁场中的电子相位的研究，简称量子霍尔效应，扩展了有序的概念。这种分类与称为拓扑学的数学分支有关，并且相被认为表现出拓扑顺序。 拓扑相位对缺陷、变形和杂质具有鲁棒性。PI将使用先进的理论方法来研究拓扑相位及其产生的原因。PI还将研究包含电子的材料和系统，这些电子彼此强烈相互作用，导致它们运动中的复杂相关性。拓扑相位的操纵可能形成计算中新范例的基础，并可能有助于未来的信息技术。该提案的教育重点旨在促进发现，促进科学教学，扩大代表性不足群体的参与，并向更广泛的公众宣传科学在我们社会福祉中发挥的核心作用。 这些目标将通过多种方式实现。其中一些是：+与高中生，特别是那些来自历史上代表性不足的群体的学生进行外联。PI将访问当地奥斯汀地区拥有大量西班牙裔/拉丁裔人口的高中，与学生和教师互动。指导女科学家。PI将参加德克萨斯大学为对物理感兴趣的有才华的女高中生举办的“爱丽丝梦游仙境”暑期项目。增加德克萨斯州K-12科学教师的数量。 PI积极参与招收本科生到科学教育专业。本科生参与研究。PI将监督本科生，因为他们追求的研究，为他们提供一个有意义的生活品味作为一个科学家。与奥斯汀当地的高科技产业合作。PI将通过与私营部门的科学家合作加强与私营部门的联系。在得克萨斯州自然科学中心与更广泛的公众接触。 PI计划公开讲座，以令人兴奋和信息丰富的方式展示研究成果。

TECHNICAL SUMMARYThis CAREER award supports an integrated program of research and education in the theory of topological and strongly correlated electronic phases of matter. Topological phases constitute a new and rapidly broadening frontier in condensed matter physics. Their robustness against imperfections and disorder make them especially promising for certain applications. The PI proposes to use a combination of analytical and numerical methods, with an emphasis on the former, to study three classes of correlated electronic states of matter:1. Strongly interacting one-dimensional systems at zero and non-zero temperature. Particular emphasis will be placed on the regime of highly thermalized spin degrees of freedom. Various aspects of the so-called spin-incoherent Luttinger liquid will be studied. 2. Finite size effects in single and multi-layer fractional quantum Hall systems. Phases that realize non-Abelian quasi-particle statistics will receive the most attention and effort will be placed on developing proposals to experimentally identify their existence. 3. Quantum liquids and topological insulators. The PI proposes to study the role of spin-orbit coupling in the realization and stabilization of different types of matter exhibiting topological order. The educational focus of this proposal seeks to advance discovery, promote teaching in the sciences, broaden participation of under represented groups, and inform the broader public about the central role science plays in the well being of our society. These goals will be accomplished in a number of ways. Among them are:+ Outreach to high school students, particularly those from historically underrepresented groups. The PI will visit local Austin-area high schools with large Hispanic/Latino populations to interact with students and teachers.+ Mentoring of female scientists. The PI will participate in the University of Texas "Alice in Wonderland" summer program for talented female high school students interested in physics.+ Increasing the number of K-12 science teachers in Texas. The PI is actively involved in recruiting undergraduate students to a science education major.+ Undergraduate participation in research. The PI will supervise undergraduate students as they pursue research to provide them with a meaningful taste of life as a scientist.+ Partnership with local Austin high-tech industry. The PI will enhance contact with the private sector through collaborations with their scientists.+ Outreach to the broader public at Texas Natural Science Center. The PI plans public lectures to present research results in an exciting and informative way.NON-TECHNICAL SUMMARYThis CAREER award supports an integrated program of research and education in the theory of new states of matter. Atoms organize themselves in distinctly different ways in different materials. The carbon atoms in diamond are self-arranged differently than those in graphite giving rise to distinctly different properties. The precise mathematical concept of symmetry based on the how the crystal can be flipped, rotated, or moved in such a way that the crystal looks the same enables the classification of phases. This classification is sufficiently general to encompass crystals composed of atoms, as well as the phases of electrons in materials, for example magnetism or quantum mechanical states where electrons themselves organize into a crystal. The study of phases of electrons trapped in a plane and exposed to a strong magnetic field, concisely known as the quantum Hall effects, has expanded the concept of order. This classification is related to a branch of mathematics known as topology and the phases are said to exhibit topological order. Topological phases are robust against imperfections, deformations, and impurities. The PI will use advanced theoretical methods to study topological phases and how they arise. The PI will also study materials and systems which contain electrons that interact strongly with each other leading to complex correlations in their motions. The manipulation of topological phases may form the basis of new paradigms in computation and may contribute to future information technologies. The educational focus of this proposal seeks to advance discovery, promote teaching in the sciences, broaden participation of under represented groups, and inform the broader public about the central role science plays in the well being of our society. These goals will be accomplished in a number of ways. A few of them are:+ Outreach to high school students, particularly those from historically underrepresented groups. The PI will visit local Austin-area high schools with large Hispanic/Latino populations to interact with students and teachers.+ Mentoring of female scientists. The PI will participate in the University of Texas "Alice in Wonderland" summer program for talented female high school students interested in physics.+ Increasing the number of K-12 science teachers in Texas. The PI is actively involved in recruiting undergraduate students to a science education major.+ Undergraduate participation in research. The PI will supervise undergraduate students as they pursue research to provide them with a meaningful taste of life as a scientist.+ Partnership with local Austin high-tech industry. The PI will enhance contact with the private sector through collaborations with their scientists.+ Outreach to the broader public at Texas Natural Science Center. The PI plans public lectures to present research results in an exciting and informative way.