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

本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，提取负责几种测量输运现象的基本物理，并为未来的实验提供指导。拟议的研究将集中在三个目标上（概述如下），其中两个涉及高tc铜超导体，第三个涉及微波辐照的二维电子系统。所采用的方法范围从纯解析到数值，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，以及散射问题的部分波和Born方法。项目的第一部分是研究d波（铜）超导体中共存电荷顺序对准粒子输运的影响。最近通过扫描隧道显微镜（STM）实验显示，电荷顺序与d波超导性共存，可以显著改变准粒子谱，如果足够强，就会使节点间隙。主要研究者（PI）和学生将计算这将对低温导热系数的影响，低温导热系数是一种经常用于测量铜酸盐中准粒子动力学的探针。该项目的第二部分是研究在d波（铜）超导体的涡旋状态下，Berry相效应对准粒子从磁涡流散射的贡献。准粒子-涡旋散射问题可简化为无质量各向异性狄拉克费米子散射问题，该散射来自非中心有效势（由于在涡旋周围循环的超流），受环绕涡旋时获得的（-1）的贝里相位影响。由于贝里相位效应的贡献，使得散射截面对涡旋核的物理特性更加敏感。PI和学生将探索利用这种效应通过热输运测量来探测涡旋核心物理的方法。该项目的第三部分涉及在弱磁场中由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状态。理论预测，这种状态的特点是电流分布不均匀。PI和学生将研究非平衡过渡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：提出的研究涉及基本理论兴趣的概念，包括共存电荷和超导秩序，无质量狄拉克准粒子动力学，准粒子涡旋散射的贝里相贡献，以及微波辐射驱动的非平衡电子动力学。更广泛的影响：所有提出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。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。微波问题的研究涉及非平衡模式形成的问题，这些问题适用于广泛的物理系统。参与本项目的研究生、本科生和高中生将学到很多物理知识，并培养广泛适用的技能。非技术摘要：提出的理论研究将研究高温超导体和相关材料中的输运，物质或电荷的流动，以期获得对其新特性的理解。从高中到研究生院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.