Geometric and Topological Phenomena in Condensed Matter Systems

凝聚态系统中的几何和拓扑现象

• 批准号: 1306011
• 负责人: Michael Stone
• 金额: $ 30万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1306011&HistoricalAwards=false
• 关键词: Geometric; Topological; Phenomena; Condensed; Matter

Technical SummaryThis award supports theoretical research and education on topological insulators. The PI will show whether crystal symmetries effect a refinement of the ten-fold way classification of the bulk bands. A large portion of the research efforts will be directed at exploring the analogies between the bulk-surface connection in topological insulators and their particle and gravitational physics analogs. In particular, the solid-state systems suggest new ways of thinking about chiral and gauge anomalies in quantum field theory. This will lead to an alternative method for calculation of transport coefficients in quark-gluon plasmas. In particular some curious relations between the coefficients in anomaly polynomials and those appearing in the well-known Sommerfeld's expansion will be explored. A key ingredient in this exploration is a set of tools developed for the description of the dynamics and quantum topology of a quantum spin as a classical mechanical system. This study will show whether these "classical" tools can be extended to derive the solid-state version of the gravitational anomaly which can be used to calculate the coefficient of the thermal analogue of the quantum Hall effect. The proposed research program will have impact beyond the field of theoretical condensed matter physics by providing guidelines for building a future generation of solid-state electronic devices that might lead to quantum computers and by allowing exploration of the speculative particle physics at a much lower cost than building large accelerators. The PI will develop a web portal to expose students and the public to recent developments in condensed matter physics. Non-Technical Summary This award supports theoretical research and education on topological insulators. A complete understanding of the universe is summarized in the "standard model" of particle physics. In this model the fundamental bits of matter interact through gauge fields which are generalizations of electricity and magnetism. Some of these interactions, the "weak" force, possess the curious feature that they only affect the left-handed parts of matter. A mathematically natural way for this handedness to arise is for matter to be trapped on a surface embedded in some higher dimensional space. This notion sounds as if it belongs in a science fiction story, but in recent years quite down-to-earth studies have shown that certain crystalline insulators containing heavy elements behave in exactly this way. These "topological insulators" are only insulators on their insides. On their surfaces, electrons are free to move and conduct electricity, but they do so in a manner that forms a precise analogue of the way that quarks interact. These conducting states are of great interest, partly for practical reasons in building new generations of solid-state electronic devices that might lead to quantum computers, but also because the analogy with particle physics allows exploration of speculative particle physics at a much lower cost than building large accelerators. The PI will develop a web portal to expose students and the public to recent developments in condensed matter physics.

该奖项支持拓扑绝缘体的理论研究和教育。PI将显示晶体对称性是否影响体带的十倍方式分类的细化。 大部分的研究工作将致力于探索拓扑绝缘体中的体表面连接与其粒子和引力物理学类似物之间的类比。特别是，固态系统为量子场论中的手征反常和规范反常提供了新的思路。这将为计算夸克-胶子等离子体中的输运系数提供一种新的方法。特别是一些奇怪的异常多项式和那些出现在著名的索末菲展开系数之间的关系将进行探讨。在这个探索的一个关键因素是一套工具的动力学和量子拓扑结构的量子自旋作为一个经典的力学系统的描述。这项研究将表明这些“经典”工具是否可以扩展到推导出的引力异常，可用于计算量子霍尔效应的热模拟的系数的固态版本。 拟议的研究计划将产生超出理论凝聚态物理学领域的影响，为构建可能导致量子计算机的下一代固态电子设备提供指导方针，并允许以比构建大型加速器低得多的成本探索投机粒子物理学。PI将开发一个门户网站，让学生和公众了解凝聚态物理学的最新发展。该奖项支持拓扑绝缘体的理论研究和教育。对宇宙的完整理解概括在粒子物理学的“标准模型”中。在这个模型中，物质的基本位通过规范场相互作用，规范场是电和磁的概括。其中一些相互作用，即“弱”力，具有一个奇怪的特征，即它们只影响物质的左手部分。数学上，这种旋向性的自然产生方式是物质被困在嵌入高维空间的表面上。这个概念听起来好像只存在于科幻小说中，但近年来相当实际的研究表明，某些含有重元素的晶体绝缘体正是以这种方式工作的。这些“拓扑绝缘体”只是它们内部的绝缘体。在它们的表面上，电子可以自由移动和导电，但它们这样做的方式形成了夸克相互作用方式的精确模拟。这些导电态引起了极大的兴趣，部分原因是由于构建新一代固态电子设备的实际原因，这些设备可能会导致量子计算机，但也因为与粒子物理学的类比允许以比构建大型加速器低得多的成本探索投机粒子物理学。PI将开发一个门户网站，让学生和公众了解凝聚态物理学的最新发展。