CAREER: Novel Quantum Hall and Correlation Physics in Topological Band Structures

该职业奖支持理论研究和教育，以调查涉及拓扑能带结构的材料中的新量子霍尔和相关物理。利用量子场论、变分蒙特卡罗、精确对角化等现代量子多体技术，PI将开展四个主要研究方向：(1)探索过渡金属氧化物异质结构中物质的新相，其中可能出现各种拓扑相。这些包括在没有外部磁场的情况下可能的高温量子自旋霍尔相和相关诱导的分数量子霍尔相。(2)了解阿贝尔和非阿贝尔分数阶陈氏绝缘子和拓扑绝缘子的性质。研究将集中于构建这些状态的波函数，并了解它们的低能特性。(3)研究三维拓扑绝缘体二维狄拉克表面态的相关量子霍尔效应。(4)了解三维Weyl半金属相的量子霍尔效应和实验特征，这可能在焦绿酸酯等材料中实现。与该奖项相关的教育活动包括为本科生和研究生开发教学课程和一系列研讨会，重点是在现代凝聚态物理中发现的物质的新阶段。这些都是为了激发学生学习和积极从事物理研究。推广活动包括一系列讲座，旨在激发中学生，特别是低收入地区中学生对科学技术的兴趣。这些讲座的目的是让年轻听众了解现代科学技术史上的一些惊人进展，以及它们在我们日常生活中的作用。为了在更广泛的范围内引起人们对科学的兴趣，PI将开发一个互动网站，用于概述他的研究活动以及教学材料。该职业奖支持理论研究和教育，以调查最近发现的电子物质的新状态，这种状态出现在某些称为拓扑绝缘体的材料中。材料通常根据电子在材料中的组织方式进行分类，导致材料类型包括：金属（如果它们导电），绝缘体（如果它们不导电）和熟悉的磁铁。基本概念使这种分类更加精确。拓扑绝缘体不属于这种传统的分类方案，因此从基础科学的角度来看，它们非常重要。它们在大部分材料中都是绝缘体，但与构成现代电子学基础的普通绝缘体不同，在绝缘体的表面和边缘有一种类似金属的状态。类似金属的状态是材料的固有属性，这是电子在体中组织自己的方式的结果。这种状态承载着惊人的现象，如在材料边界上的理想电输运，而不损失任何能量。这个项目的重点是回答关于拓扑绝缘体的基本科学问题：这些拓扑相的基本性质是什么？如何在实用材料中找到它们？它们的潜在应用是什么？PI还将研究许多有前途的拓扑相候选材料，以及外部磁场对这些相的影响。拓扑绝缘体的导电表面以及拓扑绝缘体与其他材料接触时可能出现的新现象，提出了许多可能的技术应用，从新器件技术到基于量子力学态操纵的高性能计算机技术。与该奖项相关的教育活动包括为本科生和研究生开发教学课程和一系列研讨会，重点是在现代凝聚态物理中发现的物质的新阶段。这些都是为了激发学生学习和积极从事物理研究。推广活动包括一系列讲座，旨在激发中学生，特别是低收入地区中学生对科学技术的兴趣。这些讲座的目的是让年轻听众了解现代科学技术史上的一些惊人进展，以及它们在我们日常生活中的作用。为了在更广泛的范围内引起人们对科学的兴趣，PI将开发一个互动网站，用于概述他的研究活动以及教学材料。

TECHNICAL SUMMARYThis CAREER award supports theoretical research and education to investigate the new quantum Hall and correlation physics in materials involving topological band structures. Using quantum field theory, variational Monte Carlo, exact diagonalization and other modern quantum many-body techniques, the PI will pursue four main research directions:(1) Exploring novel phases of matter in transition metal oxide heterostructures, where various topological phases may emerge. These include possible high-temperature quantum spin hall phases and correlation induced fractional quantum hall phases in the absence of an external magnetic field.(2) Understanding the nature of the abelian and non-abelian fractional Chern insulators and topological insulators. The research will focus on constructing wavefunctions for these states and understanding their low energy properties.(3) Investigating correlated quantum Hall effects of the 2D Dirac surface states of a 3D topological insulator. (4) Understanding the quantum Hall effects and experimental signatures of 3D Weyl semi-metal phases, which may be realized in materials such as pyrochlore iridates.The educational activities associated with this award include developing pedagogical courses and a seminar series for undergraduate and graduate students, with emphasis on the new phases of matter discovered in modern condensed matter physics. These are intended to excite students to study and actively pursue research in physics. Outreach activities include a lecture series aimed at sparking the interest in science and technology among middle school students, especially in low-income areas. These lectures are designed to expose the young audience to some striking advances in the history of modern science and technology, and their roles in our everyday life. To generate interest in science over a broader scale, the PI will develop an interactive website for hosting an overview of his research activities as well as teaching materials. NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to investigate a recently discovered new state of electronic matter that arises in certain materials called topological insulators. Materials are often classified according to the ways electrons organize themselves within the material, leading to materials types that include: metals if they conduct electricity, insulators if they do not, and the familiar magnet. Fundamental concepts make this classification even more precise. Topological insulators lie outside this traditional classification scheme making them very important from a fundamental science perspective. They are at once an insulator in the bulk of the material, but unlike an ordinary insulator that forms the basis of modern electronics, there is a metal-like state on the surfaces and edges of the insulator. The metal-like state is an intrinsic property of the material that is a consequence of the way electrons in the bulk organize themselves. This state hosts striking phenomena such as ideal electric transport on the boundaries of the material without losing any energy. This project focuses on answering fundamental scientific questions about topological insulators: What are the fundamental properties of these topological phases? How can they be found in practical materials? What are their potential applications? The PI will also investigate many promising candidate materials for topological phases, and the effect of an external magnetic field on these phases. The conducting surfaces of topological insulators and the possibility of new phenomena that occur when a topological insulator is brought into contact with other materials, suggests many possible technological applications from new device technologies to high performance computer technologies based on the manipulation of quantum mechanical states. The educational activities associated with this award include developing pedagogical courses and a seminar series for undergraduate and graduate students, with emphasis on the new phases of matter discovered in modern condensed matter physics. These are intended to excite students to study and actively pursue research in physics. Outreach activities include a lecture series aimed at sparking the interest in science and technology among middle school students, especially in low-income areas. These lectures are designed to expose the young audience to some striking advances in the history of modern science and technology, and their roles in our everyday life. To generate interest in science over a broader scale, the PI will develop an interactive website for hosting an overview of his research activities as well as teaching materials.