CAREER: Interplay Between Superconductivity, Quantum Liquid Crystals and Topological Phases

技术总结这个职业奖项支持关于超导、量子液晶和拓扑相之间相互作用的理论研究。PI旨在了解多个不稳定性之间的相互作用，将其视为解开强关联量子材料之谜的关键挑战。这项研究是以实验为动力和基础的。它将涉及计算和分析方法。为了解决超导和量子液晶有序之间的相互作用，PI将开发和使用新的理论方法来量化在无序关联系统中观察到的纳米级电子图案中不同的空间对称性破缺。实验分辨率正在提高，实验在许多相关材料中揭示了更多这样的模式。PI的理论框架将提供一种解释新实验的方法。通过这一新措施，PI将解决高T_c超导体中局部量子液晶物理的意义。她将开发工具来测试超导相内部的量子临界性信号。为了解决拓扑相和其他两个阶之间的相互作用，PI将开发新的方法来区分不同的拓扑相，适用于有限的温度。同时，PI将继续努力确定阿贝尔和非阿贝尔分数统计的特征，这是目前已知的拓扑学阶段的最好指标。最后，PI将调查所有三种有序之间的相互作用的两个案例：Ruthenate家族和偶分母填充量子霍尔器件。该奖项的教育部分将影响三个相关群体：康奈尔大学物理系和应用物理系的本科生和研究生，全国范围内的K-12学生，以及纽约州的中学女生。对于康奈尔大学的学生，PI将开发“科学科学交流”模块，以帮助学生掌握科学写作和演示技能。该模块将成为面向本科生和研究生的传统实验室课程的永久组成部分。在康奈尔材料研究中心的帮助下，PI将开发一种名为“令人惊叹的液晶”的教育工具包，以向K-12学生展示日常技术背后的各种新兴现象。PI将与“扩展你的视野”计划的康奈尔分会合作，并在该计划中引入网络社区的方面，以鼓励女学生对科学的兴趣。这个职业奖项支持对材料的理论研究，这些材料具有由相互强烈相互作用的电子产生的紧急物质状态。电子受量子力学规则的支配。由许多强相互作用电子组成的材料显示出新的物质状态，如超导电性。在足够低的温度下，电子可以在相同的量子力学状态下集体结合在一起，这种超导状态可以导电而不耗散。物质的其他状态也是可能的。一种物质有可能接近呈现多种物质状态。这些州可能会相互竞争，导致教科书以外的材料具有不寻常的性质。这项研究项目将用理论和计算来探索物质的三种状态之间的相互作用，超导，量子液晶顺序，电子以一种方式组织自己，使它们具有类液体和类晶体属性，以及拓扑顺序。拓扑序是一个新兴的概念，它将许多粒子的量子力学状态的结构与更熟悉的粒子组织成物质状态的不同方式的概念联系起来。这些态之间的相互作用可以在高温超导体和强磁场中的电子等材料中进行，这些材料被限制在由半导体材料制成的人造结构中的平面上。PI将根据实验结果寻求发现原则和概念来描述这些状态之间的相互作用。目标是开发一个综合的理论框架，将分析方法和计算方法结合起来。该奖项的教育部分将影响三个相关群体：康奈尔大学物理系和应用物理系的本科生和研究生，全国范围内的K-12学生，以及纽约州的中学女生。对于康奈尔大学的学生，PI将开发“科学科学交流”模块，以帮助学生掌握科学写作和演示技能。该模块将成为面向本科生和研究生的传统实验室课程的永久组成部分。在康奈尔材料研究中心的帮助下，PI将开发一种名为“令人惊叹的液晶”的教育工具包，以向K-12学生展示日常技术背后的各种新兴现象。该协会将与康奈尔大学“拓展你的视野”计划的分会合作，并在该计划中引入网络社区方面的内容，以鼓励女学生对科学的兴趣。

TECHNICAL SUMMARY This CAREER award supports theoretical research on the interplay between superconductivity, quantum liquid crystals, and topological phases. The PI aims to understand the interplay among multiple instabilities, seeing it as a key challenge to unlock the mysteries of strongly correlated quantum materials. The research is motivated by and based on experiments. It will involve computational and analytical approaches.To address the interplay between superconductivity and quantum liquid crystal order, the PI will develop and use new theoretical measures for quantifying different broken spatial symmetry in nanoscale electronic patterns observed in disordered correlated systems. Experimental resolution is increasing and experiments reveal more patterns of this sort in many correlated materials. The PI's theoretical framework will provide a way to interpret new experiments. With the new measure, the PI will address the significance of local quantum liquid crystal physics in high Tc superconductors. She will develop tools to test signatures of quantum criticality inside the superconducting phase. To address the interplay between topological phases and the other two orders, the PI will develop new measures to distinguish different topological phases, that are applicable at finite temperatures. In parallel, the PI will continue the effort to identify signatures of abelian and nonabelian fractional statistics which are the best presently known indicators of toplogical phases. Finally, the PI will investigate two cases of the interplay among all three kinds of order: the ruthenate family and even-denominator-filling quantum Hall devices. The educational component of this award will impact three relevant groups: undergraduate and graduate students in Physics and Applied Physics Departments at Cornell University, K-12 students nation-wide, and middle school girls in New York state. For Cornell students, the PI will develop "Scientific Science Communication" module to equip students with scientific writing and presentation skills. The module will become a permanent component of a traditional laboratory course for undergraduate and graduate students. With assistance from the Cornell Center for Materials Research, the PI will develop an educational kit "amazing liquid crystals", in order to demonstrate the diversity of emergent phenomena underlying everyday technology to K-12 students. The PI will partner with the Cornell chapter of the "Expand Your Horizons" program and introduce a cyber community aspect to the program to encourage interest in science among female students.NONTECHNICAL SUMMARY This CAREER award supports theoretical research on materials with emergent states of matter that arise from electrons that interact strongly with each other. Electrons are governed by the rules of quantum mechanics. Materials composed of many strongly interacting electrons display new states of matter, such as superconductivity. At sufficiently low temperature, electrons can collectively join together in the same quantum mechanical state, a superconducting state that can conduct electricity without dissipation. Other states of matter are possible. It is possible that a material is close to exhibiting more than one state of matter. These states may compete with each other leading to unusual properties in materials that lie outside the textbooks. This research project will use theory and computation to explore the interplay among three states of matter, superconductivity, quantum liquid crystal order in which electrons organize themselves in such a way that they have properties that have both liquid-like and crystal-like attributes, and topological order. Topological order is an emerging concept that connects the structure of a quantum mechanical state of many particles to more familiar concepts of the distinct ways particles organize themselves into states of matter. The interplay among these states may be carried out in materials like the high temperature superconductors and electrons in a high magnetic field that are confined to a plane in artificial structures made of semiconductor materials. The PI will seek to discover principles and concepts to describe the interplay among these states based on experimental findings. The goal is to develop a comprehensive theoretical framework combining analytical and computational approaches. The educational component of this award will impact three relevant groups: undergraduate and graduate students in Physics and Applied Physics Departments at Cornell University, K-12 students nation-wide, and middle school girls in New York state. For Cornell students, the PI will develop "Scientific Science Communication" module to equip students with scientific writing and presentation skills. The module will become a permanent component of a traditional laboratory course for undergraduate and graduate students. With assistance from the Cornell Center for Materials Research, the PI will develop an educational kit "amazing liquid crystals", in order to demonstrate the diversity of emergent phenomena underlying everyday technology to K-12 students. The PI will partner with the Cornell chapter of the "Expand Your Horizons" program and introduce a cyber community aspect to the program to encourage interest in science among female students.