CAREER:Topological and Strongly Correlated Electronic Phases

技术总结这一职业奖项支持在物质的拓扑学和强相关电子相理论方面的研究和教育的综合计划。拓扑相构成了凝聚态物理学中一个新的、迅速拓宽的前沿。它们对缺陷和混乱的健壮性使它们在某些应用中特别有希望。PI建议采用解析方法和数值方法相结合的方法来研究物质的三类关联电子态：1.零温度和非零温度下强相互作用的一维系统。将特别强调高度升温的自转自由度的制度。我们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的有限尺寸效应。实现非阿贝尔准粒子统计的阶段将受到最大的关注，并将努力制定建议，从实验上确定它们的存在。3.量子液体和拓扑绝缘体。PI建议研究自旋-轨道耦合在呈现拓扑有序的不同类型物质的实现和稳定中的作用。这项建议的教育重点是促进发现，促进科学教学，扩大代表性不足群体的参与，并让更广泛的公众了解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：+面向高中生，特别是那些来自历史上代表性不足的群体的学生。国际和平协会将访问奥斯汀地区拥有大量西班牙裔/拉丁裔人口的当地高中，与学生和教师互动。+指导女性科学家。PI将参加德克萨斯大学为对物理感兴趣的才华横溢的女高中生而设的爱丽丝漫游仙境暑期计划。+增加德克萨斯州K-12科学教师的人数。PI积极参与招收理科教育专业本科生。+本科生参与研究。PI将指导本科生从事研究，为他们提供有意义的科学家生活体验。+与当地奥斯汀高科技行业合作。国际和平协会将通过与他们的科学家合作，加强与私营部门的联系。+在德克萨斯自然科学中心向更广泛的公众宣传。PI计划进行公开演讲，以一种令人兴奋和信息丰富的方式展示研究成果。非技术性总结这个职业奖项支持一个新物质理论研究和教育的综合计划。原子在不同的材料中以明显不同的方式组织起来。金刚石中的碳原子与石墨中的碳原子的自我排列方式不同，从而导致了截然不同的性质。对称性的精确数学概念基于晶体如何翻转、旋转或以使晶体看起来相同的方式移动，从而实现了对相的分类。这种分类足够普遍，包括由原子组成的晶体，以及材料中电子的相，例如磁性或电子本身组织成晶体的量子力学状态。对被困在平面中并暴露在强磁场中的电子的相的研究，简明地被称为量子霍尔效应，扩展了有序的概念。这种分类与称为拓扑学的一个数学分支有关，而这些阶段被认为表现出拓扑顺序。拓扑相对缺陷、变形和杂质具有很强的抵抗力。PI将使用先进的理论方法来研究拓扑相及其如何产生。PI还将研究含有相互强烈相互作用的电子的材料和系统，从而在它们的运动中产生复杂的关联。对拓扑相的操纵可能形成计算中新范式的基础，并可能对未来的信息技术做出贡献。这项建议的教育重点是促进发现，促进科学教学，扩大代表性不足群体的参与，并让更广泛的公众了解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。其中几个是：+面向高中生，特别是那些来自历史上代表性不足的群体的学生。国际和平协会将访问奥斯汀地区拥有大量西班牙裔/拉丁裔人口的当地高中，与学生和教师互动。+指导女性科学家。PI将参加德克萨斯大学为对物理感兴趣的才华横溢的女高中生而设的爱丽丝漫游仙境暑期计划。+增加德克萨斯州K-12科学教师的人数。PI积极参与招收理科教育专业本科生。+本科生参与研究。PI将指导本科生从事研究，为他们提供有意义的科学家生活体验。+与当地奥斯汀高科技行业合作。国际和平协会将通过与他们的科学家合作，加强与私营部门的联系。+在德克萨斯自然科学中心向更广泛的公众宣传。PI计划举办公开讲座，以一种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.