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

该职业奖支持超导、量子液晶和拓扑相之间相互作用的理论研究。PI旨在了解多种不稳定性之间的相互作用，将其视为解开强相关量子材料之谜的关键挑战。这项研究的动机和基础是实验。它将涉及计算和分析方法。为了解决超导性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措施来量化在无序相关系统中观察到的纳米级电子模式中不同的破缺空间对称性。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类模式。PI的理论框架将提供一种解释新实验的方法。通过新的测量，PI将解决局部量子液晶物理在高Tc超导体中的重要性。她将开发工具来测试超导相中的量子临界特征。为了解决拓扑相和其他两个阶之间的相互作用，PI将开发新的措施来区分不同的拓扑相，适用于有限的温度。与此同时，PI将继续努力识别阿贝尔和非阿贝尔分数统计的签名，这是目前已知的拓扑阶段的最佳指标。最后，PI将研究所有三种顺序之间相互作用的两种情况：钌酸盐家族和偶数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“科学科学传播”模块，使学生具备科学写作和演讲技巧。该模块将成为本科生和研究生传统实验课程的永久组成部分。在康奈尔材料研究中心（Cornell Center for Materials Research）的帮助下，PI将开发一套名为“神奇液晶”（amazing liquid crystals）的教育工具包，以便向K-12年级的学生展示日常技术背后的新兴现象的多样性。PI将与康奈尔大学“拓展你的视野”项目分会合作，并在该项目中引入网络社区，以鼓励女学生对科学的兴趣。该职业奖支持对具有由电子相互作用产生的物质涌现状态的材料进行理论研究。电子受量子力学规则的支配。由许多强相互作用的电子组成的材料显示出物质的新状态，例如超导性。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，这是一种超导状态，可以在不耗散的情况下导电。物质的其他状态也是可能的。一种物质可能接近于表现出一种以上的物质状态。这些状态可能会相互竞争，导致教科书之外的材料具有不寻常的特性。本研究项目将使用理论和计算来探索物质的三种状态之间的相互作用，超导性，量子液晶秩序，其中电子以一种既具有液体性质又具有晶体性质的方式组织自己，以及拓扑秩序。拓扑秩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将自己组织成物质状态的不同方式的概念联系起来。这些状态之间的相互作用可以在高温超导体等材料中进行，也可以在半导体材料制成的人工结构中被限制在一个平面上的高磁场中的电子中进行。PI将根据实验结果寻求原理和概念来描述这些状态之间的相互作用。目标是发展一个综合的理论框架，结合分析和计算方法。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“科学科学传播”模块，使学生具备科学写作和演讲技巧。该模块将成为本科生和研究生传统实验课程的永久组成部分。在康奈尔材料研究中心（Cornell Center for Materials Research）的帮助下，PI将开发一套名为“神奇液晶”（amazing liquid crystals）的教育工具包，以便向K-12年级的学生展示日常技术背后的新兴现象的多样性。PI将与康奈尔大学“拓展你的视野”项目分会合作，并在该项目中引入网络社区，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.