Theory of Highly Correlated Electronic Systems

高度相关电子系统理论

• 批准号: 0421960
• 负责人: Steven Kivelson
• 金额: --
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0421960&HistoricalAwards=false
• 关键词: Theory; Highly; Correlated; Electronic; Systems

This award supports theoretical research in fundamental condensed matter physics. The Fermi-liquid description of weakly interacting quasiparticles has been remarkably successful as a framework for treating the properties of the electron fluids encountered in a wide variety of crystalline materials and solid state devices, even where the electron-electron interactions are quite strong, and the Fermi liquid parameters are strongly renormalized from their bare values. However, there are also many cases where the Fermi liquid approach qualitatively fails: systems in which whatever dispersing feature there are in the single particle spectral functions are overdamped in the sense that their widths are larger than their mean, or where there are phase transitions to broken symmetry states with temperature and energy scales comparable to microscopic electronic scales, or that exhibit macroscopic behaviors that are inconsistent with weakly interacting quasiparticles, such as finite resistance in a two-dimensional system in the low temperature limit, or metallic(increasing with increasing temperature) resistivities with magnitudes in excess of the Ioffe-Regel limit. Non-interacting electrons serve as the appropriate paradigmatic for well developed Fermi liquids, but simple, solvable models of strongly interacting electrons are few and far between. It is the principle purpose of the research envisaged here to obtain well controlled approximate, or even asymptotically exact solutions to simple models of strongly interacting electrons as a step in filling this void. More particularly, it is proposed to study models with purely repulsive interactions between electrons in which the existence of a superconducting state with a high transition temperature can be firmly established and the transition temperature reliably estimated. This study is relevant to elucidating the mechanism of high temperature superconductivity. On a more phenomenological level, it is proposed to study the effects of electronic micro-phase-separation, a common occurrence in strongly correlated "bad metals," on various macroscopic properties such as the optical conductivity and DC transport. While much of this effort is inspired by an attempt to understand the remarkable properties of the cuprate high temperature superconductors, applications of related ideas to low density electron gases in MOSFET's, and to other highly correlated electronic materials, such as transition metal oxides and the organic superconductors, are also planned.There are, by now, many examples of highly correlated bad metals, where conventional approaches to the theory of electronic structure fail. Obtaining a simple, qualitative understanding of these materials is an intellectual question on par with, "What is a metal?" High temperature superconductivity is only one of the phenomena observed in such materials, but one of the most exciting.This work will serve as a fertile source of research projects for students. The problems are well defined, and of direct experimental relevance, while at the same time involving mastery of a large number of methods of many body physics. %%%This award supports theoretical research on fundamental condensed matter physics. The topic is materials which exhibit strongly interacting electrons which produce effects, such as high temperature superconductivity, that are unable to be understood with current theory. A systematic procedure will be followed to develop and solve models, including experimental predictions, which will contribute to the understanding of these materials. As part of this project, students will be trained in modern techniques of condensed matter theory.***

该奖项支持基础凝聚态物理的理论研究。 弱相互作用准粒子的费米液体描述作为处理各种晶体材料和固态器件中遇到的电子流体特性的框架已经非常成功，即使在电子-电子相互作用相当强的情况下也是如此。费米液体参数从其裸值强烈重整化。 然而，在许多情况下，费米液体方法在质量上是失败的：在系统中，单粒子谱函数中存在的任何色散特征都被过阻尼，因为它们的宽度大于其平均值，或者存在相变到温度和能量尺度与微观电子尺度相当的对称破缺态，或者表现出与弱相互作用准粒子不一致的宏观行为，例如低温极限下二维系统中的有限电阻，或金属电阻率（随温度升高而增加），其大小超过 Ioffe-Regel 极限。 非相互作用电子是发展良好的费米液体的适当范例，但简单、可解的强相互作用电子模型却很少。 这里设想的研究的主要目的是获得强相互作用电子的简单模型的良好控制的近似解，甚至渐近精确的解，作为填补这一空白的一步。 更具体地，建议研究电子之间具有纯粹排斥相互作用的模型，其中可以牢固地建立具有高转变温度的超导状态的存在并且可靠地估计转变温度。 这项研究与阐明高温超导机理有关。 在更现象学的层面上，建议研究电子微相分离（在强相关的“坏金属”中常见）对各种宏观特性（例如光导率和直流输运）的影响。 虽然这项工作的大部分灵感来自于尝试了解铜酸盐高温超导体的卓越特性，并将相关想法应用于 MOSFET 中的低密度电子气，以及其他高度相关的电子材料，例如过渡金属氧化物和有机材料。超导体也在计划中。到目前为止，有许多高度相关的不良金属的例子，而传统的电子结构理论方法却失败了。 对这些材料获得简单、定性的理解是一个与“什么是金属？”同等的智力问题。 高温超导只是在此类材料中观察到的现象之一，但却是最令人兴奋的现象之一。这项工作将为学生的研究项目提供丰富的来源。 这些问题定义明确，具有直接的实验相关性，同时涉及对许多身体物理学的大量方法的掌握。 %%%该奖项支持基础凝聚态物理的理论研究。 该主题是表现出强烈相互作用的电子的材料，这些电子产生的效应（例如高温超导性）是当前理论无法理解的。 将遵循系统程序来开发和解决模型，包括实验预测，这将有助于理解这些材料。 作为该项目的一部分，学生将接受凝聚态理论现代技术的培训。***