Low Temperature Transport in Cuprate Superconductors and Microwave-Irradiated Two-Dimensional Electron Systems

这个理论项目的目标是通过执行与感兴趣的系统相关的低温输运计算，提取对几个测量到的输运现象负责的基本物理，并为未来的实验提供指导。拟议的研究将集中于三个目标(概述如下)，其中两个目标涉及高T_c铜酸盐超导体，第三个目标涉及微波辐射的二维电子系统。所用的方法从纯解析到数值，包括平衡和非平衡图解Kubo公式计算，半经典方法，电动力学稳定性分析，Bogoliubov-de Gennes方程的解，以及散射问题的分波和Born方法。项目的第一部分是研究共存电荷顺序对d波(铜酸盐)超导体中准粒子输运的影响。最近通过扫描隧道显微镜(STM)实验表明，电荷顺序与d波超导电性共存，如果足够强，可能会显著改变准粒子光谱，使节点裂开。主要研究人员(PI)和学生们将计算这将对低温热导率的影响，低温热导率通常被用来测量铜氧化物中准粒子的动力学。该项目的第二部分是研究贝里相位效应对d波(铜酸盐)超导体涡旋态磁涡中准粒子散射的贡献。准粒子-涡旋散射问题归结为无质量各向异性狄拉克-费米子对非中心有效势的散射问题(由于超流在涡旋周围循环)，使涡旋旋转时获得的Berry位相为(-1)。Berry位相效应的贡献应使散射截面对涡核的物理性质敏感。PI和学生们将探索如何利用这种效应通过热输运测量来探测涡旋核心物理。该项目的第三部分涉及在弱磁场中微波辐射驱动的高迁移率二维电子系统中观察到的零电阻态。理论预测，这种状态的特征是电流分布不均匀。PI和学生将研究非平衡转变到这种状态的动力学，由此产生的电流分布的结构，以及其波动的性质。智力优势：拟议的研究涉及基本理论感兴趣的概念，包括共存电荷和超导秩序，无质量狄拉克准粒子的动力学，Berry相对准粒子涡旋散射的贡献，以及微波辐射驱动的非平衡电子动力学。广泛影响：所有拟议的计算都受到最近实验的启发，旨在解释测量到的输运现象，并为未来的实验提供指导。因此，潜在的影响远远大于计算本身的范围。关于铜酸盐中准粒子输运的研究旨在为解决铜酸盐问题本身这一更大的问题提供线索。关于微波问题的工作涉及到适用于广泛物理系统的非平衡图案形成问题。参与该项目的研究生、本科生和高中生将学习许多物理知识，发展广泛的适用技能。非技术摘要：拟议的理论研究将研究高温超导体及相关材料中的输运，即物质或电荷的流动，以期了解它们的新性质。从高中到研究生的学生都将参与其中。

The goal of this theoretical project is to extract the essential physics responsible for several measured transport phenomena by performing low temperature transport calculations relevant to the systems of interest and providing guidance for future experiments. The proposed research will focus on three objectives (outlined below), two of which concern the high-Tc cuprate superconductors and the third which concerns microwave-irradiated two-dimensional electron systems. Methods employed range from purely analytical to numerical and include equilibrium and non-equilibrium diagrammatic Kubo formula calculations, semi-classical approaches, electrodynamical stability analyses, solution of the Bogoliubov-de Gennes equation, and partial wave and Born approaches to scattering problems.The first part of the project is a study of the influence of coexisting charge order on quasiparticle transport in a d-wave (cuprate) superconductor. Charge order, recently shown via scanning tunneling microscopy (STM) experiments to coexist with the d-wave superconductivity, could significantly alter the quasiparticle spectrum, gapping out the nodes if sufficiently strong. The principle investigator (PI) and students will calculate the effect this will have on low temperature thermal conductivity, a probe frequently employed to measure the dynamics of quasiparticles in the cuprates.The second part of the project is a study of the contribution of Berry phase effects to the scattering of quasiparticles from magnetic vortices in the vortex state of a d-wave (cuprate) superconductor. The quasiparticle-vortex scattering problem reduces to that of a massless anisotropic Dirac fermion scattering from a non-central effective potential (due to the superflow circulating around the vortex) subject to the Berry phase of (-1) acquired upon circling the vortex. The contribution of Berry phase effects should make the scattering cross-section sensitive to the physics of the vortex core. The PI and students will explore ways to use this effect to probe vortex core physics via thermal transport measurements.The third part of the project concerns the zero-resistance states observed in high-mobility two-dimensional electron systems driven with microwave radiation in a weak magnetic field. Theory predicts that such states are characterized by an inhomogeneous distribution of current flow. The PI and students will study the kinetics of the non-equilibrium transition into this state, the structure of the resulting current distribution, and the nature of its fluctuations.Intellectual merit: The proposed research involves concepts of basic theoretical interest including coexisting charge and superconducting order, dynamics of massless Dirac quasi-particles, Berry phase contribution to quasiparticle-vortex scattering, and non-equilibrium electron dynamics driven by microwave radiation.Broader impact: All of the proposed calculations were inspired by recent experiments and are intended to explain measured transport phenomena and provide guidance for future experiments. Hence, there is potential for impact much larger than the scope of the calculations themselves. Work on quasiparticle transport in the cuprates is intended to provide clues to the larger issue of solving the cuprate problem itself. Work on the microwave problem touches on issues of non-equilibrium pattern formation which apply to a broad range of physical systems. Graduate, undergraduate, and high school students involved in this project will learn much physics and develop a wide range of broadly applicable skills.Non-Technical Abstract:The theoretical research proposed will study transport, the flow of matter or charge, in high temperature superconductors and related materials in hopes of gaining an understanding of their novel properties. Students ranging from high school to graduate school will be involved.