Time Dependence and Textures in Low Dimensional Electron Systems

非技术性总结：该奖项支持关于特殊安排的外部干扰在材料中创建新颖电子状态的作用的理论研究和教育。在凝聚态系统的背景下，拓扑学提供了一种理解电子如何在材料中组织的方法，以及预测它们如何穿过和沿着材料边缘移动的鲁棒特性。这个概念已经越来越被认为是凝聚态系统物理学的一个重要方面。在这个项目中，PI将探索如何使用周期性的时间依赖性扰动来操纵材料中电子状态的拓扑特征，例如随时间变化的光或电场和磁场。由此产生的系统通常被称为Floquet系统，它们都具有支持“纹理”的能力，在这些区域中，离散的属性（例如电子的内在磁性方向）以不同的方式变化，当将系统作为一个整体组合时，会导致具有有趣属性的模式。该研究的重点是如何理解和预测这种模式应该存在的时候，并进一步开发有用的模型，这种微观特性的重组和图案化如何导致可测量的电子后果。PI还将在Floquet系统的情况下探索利用纹理作为量子信息处理中可能资源的可能性。该项目将在研究生的充分参与下进行，他们将接受凝聚态物理学现代方法的培训，为他们在科学和技术领域的职业生涯做准备。来自美国和国外的科学家将共同参与这项工作。此外，PI还将参与一项专门针对印第安纳州农村和/或低收入地区高中生的教育计划：为无法获得大学先修物理课程的印第安纳州高中生创建在线物理入门课程。包括将讨论与此提案相关的显着的现代材料，如石墨烯和碳纳米管。技术摘要：该奖项支持Floquet材料中拓扑结构作用的理论研究和教育。Floquet系统由周期性的时间相关势定义，例如通过将强的圆偏振光正常照射到二维电子系统上。在某些情况下，这样的潜力可以诱导纹理和拓扑结构的状态，这可能不存在，或可能有不同的形式，在相应的静态系统的带。PI试图回答有关这些系统的基本问题。这项研究将包括研究边态结构和输运性质，这似乎是在一个更复杂的方式比类似的静态拓扑系统。作为其中的一部分，PI和同事将探索直接解决传输系数的拓扑不变量，并研究它们如何与它们支持的边缘状态相关。将进行无序效应的研究，包括不同拓扑状态之间的局域化和无序诱导的转变。还将探讨新的概念，在光学产生的“谷电子学”，这可能是实现某些Floquet系统。这些研究还将包括更简单的模型，着眼于定义Floquet系统的密度矩阵，最终目标是开发方法，其中接触和/或热浴不需要明确包括在Floquet系统建模中。纹理也可以存在于真实的空间中，并且在量子霍尔系统中具有特别有趣的实现，因为它们携带物理电荷。在该项目中，这种物理学将在多组分狄拉克系统中进行探索，特别是石墨烯和拓扑绝缘体表面，其中不同的可能的对称性破缺可能会竞争产生最低能量的基态。通过从整数填充中掺杂这种系统而引入的纹理应该导致在空间非均匀图案中联合收割机组合不同类型的排序的状态。这些系统提供了丰富的相图和新颖的转变，量子和热，不同的阶段之间。主要研究者和合作者将寻求充分描述和理解此类系统。此外，薄拓扑绝缘体的边缘理论的相互作用诱导横向表面之间的相干性的探索将进行。这影响了边缘电子的光谱和物理行为，无论是在平均场水平，还是当表面有序的波动被纳入时。该项目将在研究生的全面参与下进行，他们将接受凝聚态物理学的现代方法的培训，为他们在科学和技术领域的职业生涯做好准备。来自美国和国外的科学家将共同参与这项工作。此外，PI还将参与一项专门针对印第安纳州农村和/或低收入地区高中生的教育计划：为无法获得大学先修物理课程的印第安纳州高中生创建在线物理入门课程。包括将讨论与这一建议相关的显着的现代材料，如石墨烯和碳纳米管。

NON-TECHNICAL SUMMARY: This award supports theoretical research and education on the role of specially arranged external disturbances in creating novel electronic states in materials. Topology in the context of condensed matter systems provides a way of understanding how electrons are organized in a material, as well as predicting robust properties of how they move through and along the edges of the material. The concept has become increasingly recognized as an important facet of the physics of condensed matter systems. In this project, the PI will explore how topological characteristics of electronic states in materials can be manipulated using periodic time-dependent disturbances, such as light or electric and magnetic fields that vary in time. The resulting systems are generically known as Floquet systems, and they share the ability of supporting "textures," regions where discrete properties, such as the direction of the intrinsic magnetism of the electron, vary in ways which, when combined for the system as a whole, lead to patterns with interesting properties. The research is focused on ways to understand and predict when such patterns should be present, and furthermore in developing useful models of how such reorganization and patterning of microscopic properties leads to measurable electronic consequences. The PI will also explore, in the case of Floquet systems, the possibility of exploiting textures as possible resources in quantum information processing. This project will be conducted with the full participation of graduate students, who will be trained in modern methods of condensed matter physics, preparing them for careers in science and technology. Scientists from the US and abroad will be collaboratively involved in the work. In addition, the PI will be involved in an educational initiative specifically for high-school students from rural and/or low-income areas in Indiana: the creation of an online introductory physics course for Indiana high-school students without access to an Advanced Placement physics course. Included will be discussions about the remarkable modern materials relevant to this proposal, such as graphene and carbon nanotubes.TECHNICAL SUMMARY: This award supports theoretical research and education on the roles of topology in Floquet materials. Floquet systems are defined by periodic time-dependent potentials, for example by shining strong, circularly polarized light normally onto a two dimensional electron system. In some cases such potentials can induce texture and topology in a band of states, which may not be present, or may have a different form, in the corresponding static system. The PI seeks to answer fundamental questions about these systems. The research will include studies of edge-state structure and transport properties, which appear to be related in a more complicated way than in analogous static topological systems. As part of this, the PI and coworkers will explore topological invariants that directly address transport coefficients, and investigate how they relate to the edge states they support. Studies of disorder effects, including localization and disorder-induced transitions among different topological states, will be undertaken. Also explored will be new concepts in optically generated "valleytronics" which might be realized for certain Floquet systems. The studies will also include simpler models with an eye towards defining density matrices for Floquet systems, with the eventual goal of developing methods in which contacts and/or thermal baths need not be explicitly included in modeling a Floquet system. Textures can also be present in real space, and have particularly interesting realizations in quantum Hall systems, for which they carry physical charge. In the project, such physics will be explored in multicomponent Dirac systems, in particular graphene and topological insulator surfaces, where different possible broken symmetries may compete to yield the lowest energy ground state. Textures introduced by doping such systems away from integer fillings should result in states that combine different types of orderings in spatially non-uniform patterns. These systems offer rich phase diagrams and novel transitions, both quantum and thermal, between different phases. The PI and collaborators will seek to fully characterize and understand such systems. In addition, an exploration of edge theories of thin topological insulators in which interactions induce coherence between transverse surfaces will be conducted. This impacts the spectrum and physical behavior of electrons at the edge both at the mean-field level, and when fluctuations of the surface ordering are incorporated.This project will be conducted with the full participation of graduate students, who will be trained in modern methods of condensed matter physics, preparing them for careers in science and technology. Scientists from the US and abroad will be collaboratively involved in the work. In addition, the PI will be involved in an educational initiative specifically for high-school students from rural and/or low-income areas in Indiana: the creation of an online introductory physics course for Indiana high-school students without access to an Advanced Placement physics course. Included will be discussions about the remarkable modern materials relevant to this proposal, such as graphene and carbon nanotubes.