Electron Transport in Low-Dimensional and Mesoscopic Topological Solids

非技术性总结该奖项支持旨在开发理论工具以表征和利用各种技术相关材料特性的研究。从手持设备的可弯曲屏幕到未来的量子信息机器，量子电子学的进步取决于具有理想机械和电气特性的材料的开发。近几十年来，材料物理学在实验和理论上都有了重大发现。石墨烯是一种从石墨中分裂出来的一个原子厚的二维晶体，它的分离促进了由各种其他元素制成的新二维材料的发现。拓扑固体的理论预测-导体，半导体和绝缘体具有非常不寻常的电子特性-为在实验室中合成这些新材料铺平了道路。它们中的一些是真正独特的，自然地结合了绝缘体的性质和导体的性质。这种材料发现的快速进展要求发展新的理论方法来理解这些新材料的性质，解释实验结果，并帮助指导新的实验发现。本项目旨在建立实现这些目标所需的理论，研究一系列新型低维拓扑材料的导电和微波响应特性。这些特性与材料的独特电子结构及其电荷载流子的动力学有关。三个具体的研究方向包括低维拓扑超导体的微波性质，二维拓扑固体中的电子输运理论，以及一类拓扑导体（称为Weyl金属）的磁性和电子特性。研究生将积极参与研究;他们将在广泛的理论技术指导和培训。PI还计划提供一套讲座介绍前沿的量子材料理论的非专业观众。技术总结该奖项支持的研究是集中在理论研究的直流和交流响应函数的几个低维和介观系统与非平凡的带拓扑。重点放在理论适用于实验与超导纳米电路，平带二维导体，外尔半金属表面。该项目的动机来自于新材料合成的进步，实验技术使静态和动态响应的高精度测量成为可能，以及评估这些响应对理论提出的挑战。该项目的第一部分致力于开发研究拓扑超导相的新方法。这一部分的主要目标是阐明无序和超导相的拓扑结构对大块超导体及其结的微波响应函数的联合作用。该项目的第二部分旨在发展窄带二维导体中电子的流体动力学理论，有或没有自发破缺的对称性。我们的目标是了解最近测量的隧道光谱，预测在约束几何的电子流模式，并找到相应的电导。该项目的第三部分解决了与外尔金属表面相关的运输和热力学性质的磁振荡。目标是确定与表面相关的电导率和磁化率的振荡贡献，但不依赖于连接相对表面的电子轨迹。该项目的所有部分都面向实验介观物理的需要。解决该项目中提出的问题有望解释现有的实验结果，帮助规划新的实验，并开发广泛适用于低维量子凝聚态的理论方法。研究生将积极参与研究;他们将在广泛的理论技术指导和培训。PI还计划举办一系列讲座，向非专业观众介绍量子材料理论的前沿。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports research that is aimed at developing theoretical tools for characterizing and harnessing the properties of various technologically relevant materials. Progress in quantum electronics, from bendable screens of hand-held devices to future quantum information machines, hinges on the development of materials with desirable mechanical and electrical properties. Recent decades have brought remarkable experimental and theoretical discoveries in the physics of materials. Isolation of graphene, a one-atom thick two-dimensional crystal cleaved out of graphite, boosted the discovery of new two-dimensional materials made out of various other elements. Theoretical prediction of topological solids – conductors, semiconductors, and insulators with highly unusual electronic properties – have paved the way for the synthesis of these novel materials in the laboratory. Some of them are truly unique by naturally combining the properties of an insulator in the bulk and of a conductor at the surface. The rapid progress in such materials discovery calls for the development of new theoretical methods to understand the properties of these novel materials, explain experimental findings, and help in guiding new experimental discoveries. This project aims at building the theory needed to achieve these goals.The research addresses a set of electrical conduction and microwave response characteristics of novel low-dimensional topological materials. These characteristics are associated with the materials’ unique electronic structure and with the dynamics of their charge carriers. The three specific directions of the research cover the microwave properties of low-dimensional topological superconductors, theory of electron transport in two-dimensional topological solids, and magnetic and electronic characteristics of a class of topological conductors, called Weyl metals. Graduate students will be actively involved in the research; they will be mentored and trained in a broad range of theoretical techniques. The PI also plans to deliver a set of lectures introducing the frontiers of quantum materials theory to non-expert audiences.TECHNICAL SUMMARYThis award supports research that is focused on theoretical investigations of the dc and ac response functions of several low-dimensional and mesoscopic systems with nontrivial band topology. The emphasis is placed on theory applicable to experiments with superconducting nano-circuits, flat-band two-dimensional conductors, and surfaces of Weyl semimetals. The motivation comes from the advances in synthesis of new materials, experimental techniques enabling the high precision measurements of static and dynamic responses, and from the challenges the evaluation of these responses presents for the theory.The first part of the project is devoted to developing new methods of studying topological superconducting phases. The main goal of this part is to elucidate the joint effect of disorder and topology of a superconducting phase on the microwave response functions of bulk superconductors and their junctions. The second part of the project aims at developing a hydrodynamic theory of electrons in narrow-band two-dimensional conductors, with or without spontaneously-broken symmetries. The goal is to understand the recently-measured tunneling spectra, predict the electron flow patterns in constrained geometries, and find the corresponding conductance. The third part of the project addresses the magnetic oscillations of the transport and thermodynamic properties associated with a surface of a Weyl metal. The goal is to identify the oscillatory contributions to conductivity and magnetic susceptibility which are associated with a surface, but do not rely on electron trajectories connecting the opposite surfaces.All parts of the project are geared towards the needs of experimental mesoscopic physics. Solving the problems formulated in the project is expected to explain existing experimental results, help in planning new experiments, and develop theoretical methods broadly applicable to low-dimensional quantum condensed matter. Graduate students will be actively involved in the research; they will be mentored and trained in a broad range of theoretical techniques. The PI also plans to deliver a set of lectures introducing the frontiers of quantum materials theory to non-expert audiences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.