Theory of Highly Correlated Electronic Systems

高度相关电子系统理论

• 批准号: 0531196
• 负责人: Steven Kivelson
• 金额: --
• 依托单位: Stanford University
• 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: 2004-09-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0531196&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一种框架，已经非常成功地处理了在各种晶体材料和固态器件中遇到的电子流体的性质，即使在电子-电子相互作用相当强的情况下，费米液体参数也从它们的裸值强烈地重整化。然而，也有许多情况下，费米液体方法定性地失败：在系统中，无论在单个粒子谱函数中有什么色散特征，它们的宽度都比它们的平均值大，或者存在到破坏对称态的相变，其温度和能量尺度与微观电子尺度相当，或者表现出与弱相互作用准粒子不一致的宏观行为，例如，在低温极限下的二维系统中的有限电阻，或者超过Ioffe-Regel极限的大小的金属(随温度增加)电阻率。对于发展良好的费米液体来说，非相互作用电子是合适的范例，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简单的强相互作用电子模型的良好控制的近似解，甚至渐近精确解，作为填补这一空白的一步。更具体地说，建议研究电子之间存在纯排斥相互作用的模型，在这些模型中，可以确定具有高转变温度的超导态的存在，并且可靠地估计转变温度。这一研究对于阐明高温超导电性的机制具有重要意义。在更唯象的水平上，建议研究电子微观相分离对各种宏观性质的影响，如光学导电性和直流输运。虽然这项工作的大部分灵感来自于试图了解铜酸盐高温超导体的显著性质，但相关概念也计划应用于MOSFET中的低密度电子气，以及其他高度相关的电子材料，如过渡金属氧化物和有机超导体。到目前为止，有许多高度相关的不良金属的例子，其中电子结构理论的传统方法无效。对这些材料有一个简单的、定性的理解，这是一个智力问题，就像“什么是金属？”高温超导只是在这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。这项工作将成为学生研究项目的肥沃来源。这些问题定义明确，具有直接的实验相关性，同时涉及掌握许多身体物理学的大量方法。该奖项支持基础凝聚态物理的理论研究。这个主题是显示出强相互作用电子的材料，这些电子产生的效应，如高温超导，无法用当前的理论来理解。将遵循一个系统的程序来开发和求解模型，包括实验预测，这将有助于理解这些材料。作为这个项目的一部分，学生们将接受现代凝聚态理论技术的培训。