Interactions and Disorder in One-, Two-, and Three-Dimensional Systems

一维、二维和三维系统中的相互作用和无序

• 批准号: 0308377
• 负责人: Dmitrii Maslov
• 金额: $ 24万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308377&HistoricalAwards=false
• 关键词: Interactions; Disorder; Two; Three; Dimensional

The common theme of this theoretical research is the interplay between electron-electron interactions and the disorder in one-, two-, and three-dimensional systems. Such an interplay is at the core of many, if not all, phenomena that define the current agenda in the fields of strongly-correlated and mesoscopic systems including high-Tc materials, new phases in two-dimensional systems with and without magnetic field, quantum dots, carbon nanotubes, etc.A combination of strong interactions, disorder and reduced dimensionality may result in a significant deviation from or even a complete breakdown of the Fermi-liquid state. Non-Fermi-liquid metals are the subject of intensive studies in many subfields of condensed matter physics. An important, and in many cases only, tool for studying the Fermi-liquid state of a metal or its breakdown are the magneto-oscillations in thermodynamic and transport properties. For a Fermi liquid, the pattern of these oscillations encodes the principal parameters of the state, such as the effective mass and spin susceptibility. The first part of this project is devoted to the reconsideration of the theory of magneto-oscillations in a two-dimensional disordered, interacting system. Such a study is particularly relevant in view of recent experiments aimed at characterizing the state of electrons in semiconductor heterostructures which exhibit an unexpected metal-insulator transition, and is also of fundamental importance on its own footing. Although it is known that the conventional description of magneto-oscillations breaks down in two-dimensions, a comprehensive theory which replaces the conventional one and allows detailed comparison with experiment will be very useful.The peculiarity of a two-dimensional, interacting system is that even a relatively weak magnetic field leads to a non-perturbative reconstruction of the ground state. The theme of a magnetic-field induced reconstruction of the ground state is continued in the second part of the project that deals with three-dimensional metals in a strong magnetic field. In the extreme limit, when only the lowest Landau level remains populated, the magnetic field is known to induce instabilities of the ground state with respect to, e.g., spin-and charge-ordering or exciton pairing. It has recently been shown that the excitations of such a system behave similarly to those of a one-dimensional Luttinger liquid. This research aims at constructing a theory of transport in the "magnetic-field-induced Luttinger liquid." Also, there is a pressing need to develop the theory of dephasing in a strong magnetic field. The last part of the project is on Anderson localization and dephasing on one-dimensional systems and is related to the second part of the research project.Graduate students will be involved the project and will receive training in both solving the fundamental problems and applying them to understand experiments. Results will be incorporated into the graduate course on modern condensed matter physics that the PI teaches.%%%The common theme of this theoretical research is the interplay between electron-electron interactions and the disorder in one-, two-, and three-dimensional systems. Such an interplay is at the core of many, if not all, phenomena that define the current agenda in the fields of strongly-correlated and mesoscopic systems including high-Tc materials, new phases in two-dimensional systems with and without magnetic field, quantum dots, carbon nanotubes, etc. Graduate students will be involved the project and will receive training in both solving the fundamental problems and applying them to understand experiments. Results will be incorporated into the graduate course on modern condensed matter physics that the PI teaches.***

这种理论研究的共同主题是电子-电子相互作用和一维，二维和三维系统中的无序之间的相互作用。 这种相互作用是许多（如果不是全部的话）现象的核心，这些现象定义了强相关和介观系统领域的当前议程，包括高Tc材料、具有和不具有磁场的二维系统中的新相、量子点、碳纳米管等。无序和降低的维数可能导致费米液体状态的显著偏离或甚至完全崩溃。 非费米液态金属是凝聚态物理学许多子领域的深入研究对象。 研究金属的费米液体状态或其击穿的一个重要工具是热力学和输运性质中的磁振荡。 对于费米液体，这些振荡的模式编码状态的主要参数，如有效质量和自旋磁化率。 这个项目的第一部分是致力于在一个二维无序，相互作用系统的磁振荡理论的反思。 这样的研究是特别相关的，鉴于最近的实验，旨在表征半导体异质结构中的电子状态，表现出意想不到的金属-绝缘体过渡，也是其自身的立足点的根本重要性。 虽然我们知道磁振荡的传统描述在二维空间中是失效的，但是用一个全面的理论来代替传统的理论，并允许与实验进行详细的比较，这将是非常有用的。二维相互作用系统的特点是，即使是一个相对较弱的磁场也会导致基态的非微扰重构。 磁场诱导的基态重建的主题在该项目的第二部分中继续进行，该部分涉及强磁场中的三维金属。 在极端极限中，当仅最低的朗道能级保持被填充时，已知磁场引起基态相对于例如，自旋和电荷排序或激子配对。 它最近已被证明，这样一个系统的激发行为类似的一维Luttinger液体。 本研究旨在建立一个“磁场诱导Luttinger液体”的输运理论。“此外，迫切需要发展强磁场中的失相理论。 本计画的最后一部分是关于一维系统的安德森定域与退相，并与研究计画的第二部分有关。研究生将参与本计画，并将接受解决基本问题与应用它们来理解实验的训练。 研究结果将纳入PI教授的现代凝聚态物理学研究生课程。%这种理论研究的共同主题是电子-电子相互作用和一维，二维和三维系统中的无序之间的相互作用。 这种相互作用是许多（如果不是全部）现象的核心，这些现象定义了强相关和介观系统领域的当前议程，包括高Tc材料，有和没有磁场的二维系统中的新相，量子点，碳纳米管，研究生将参与该项目，并将接受解决基本问题和应用它们来理解实验 研究结果将纳入PI教授的现代凝聚态物理学研究生课程。