拓扑量子系统中近藤效应的研究

发布时间：2018-03-14 23:10

本文选题：近藤效应　切入点：拓扑量子系统　出处：《南京大学》2017年博士论文　论文类型：学位论文

【摘要】：自上个世纪六十年代以来,近藤效应及其相关的物理问题一直是凝聚态理论中一个重要的研究热点。相关早期研究不仅促进了重整化群理论方法的建立,而且推动并发展了基于数值重整化群的一系列数值计算方法。另一方面,近年来由于在量子输运、拓扑量子计算等方向的潜在应用价值,拓扑量子态物质逐渐发展成为凝聚态物理中最重要的研究课题之一。多种拓扑材料包括拓扑绝缘体、拓扑半金属等均已经在实验上实现。一个理论上有趣且具有实际意义的问题是,在新颖的拓扑量子相中,传统的近藤效应会产生什么新的物理?近藤共振、近藤温度等是否会和传统金属中的近藤效应有所区别?近藤单态的形成是否有可能诱导出新的拓扑量子态?一旦结合上拓扑量子系统,传统的近藤问题将会产生一系列与之相关的新的有趣问题。本文主要目的就是初步探索并回答这些问题。第一章我将为本文即将研究的两个课题做出简要概述。对于近藤问题,我从研究历史的角度出发,阐述了它的发展过程,回顾了历史中重要的进展。对于拓扑量子系统,我主要试图回答拓扑是什么以及怎么去刻画拓扑态。第二章是关于近藤效应的微扰处理。首先我针对非磁性杂质问题讨论了T矩阵解法。接着利用T矩阵方法处理了无相互作用的安德森模型。对于安德森模型和s-d交换模型,我们采用近藤提出的微扰方法给出初步解释。同时也可以看到在微扰理论的框架下,计算出的电阻等物理量在低温区总是发散。这不符合实验结果。这就迫使我们必须去寻找非微扰方法。第三章主要是阐述几种非微扰方法。为此我们先讨论了赝费米子表示和微扰重整化群。接着我们详细给研究了非微扰重整化的理论方案以及Bethe ansatz严格解方法。在第四章中,我将针对低温强耦合区建立一个有效理论。我们发现在强耦合区可以用一个弱耦合的朗道费米液体理论来刻画这个不动点。这种特定能标下的有效理论正是重整化群思想的核心。从第五章起至第八章,我主要讨论了近藤效应在拓扑量子系统中的相关研究与应用。第五章主要是介绍当前在该领域的研究现状。第六章到第八章分别是三个具体的研究实例。从这些章节,我们可以看到,近藤效应尽管是一个已经有半个多世纪历史的研究课题,当它和新的拓扑态系统相结合后,不仅会展现出与传统近藤效应不同的物理特征,同时也可能产生出更多新颖的拓扑量子态。
[Abstract]:Since -40s, Kondo effect and its related physical problems have been an important research hotspot in condensed matter theory. Moreover, a series of numerical methods based on renormalization groups have been developed. On the other hand, in recent years, due to their potential applications in quantum transport and topological quantum computing, Topological quantum state matter has gradually developed into one of the most important research topics in condensed matter physics. One interesting and practical question in theory is: what new physics will the traditional Kondo effect produce in a novel topological quantum phase? Kondo resonance, Kondo temperature and so on will be different from the traditional metal Kondo effect? Is it possible to induce a new topological quantum state by the formation of a single state of Kondo? Once combined with the topological quantum system, The traditional Kondo question will produce a series of new and interesting questions related to it. The main purpose of this paper is to explore and answer these questions. In Chapter 1, I will give a brief overview of the two topics to be studied in this paper. From the perspective of studying history, I described its development process and reviewed the important progress in history. I mainly try to answer what topology is and how to depict the topological state. Chapter 2 is about the perturbation treatment of Kondo effect. First, I discuss the solution of T matrix for nonmagnetic impurity problem. Then I use T matrix method to solve the problem of nonmagnetic impurity. For Anderson model and s-d exchange model, We use the perturbation method proposed by Kondo to give a preliminary explanation. At the same time, we can see that in the framework of perturbation theory, The calculated physical quantities such as resistors always diverge in the low temperature region. This does not accord with the experimental results. This forces us to find non-perturbation methods. Chapter 3 mainly describes several non-perturbation methods. For this reason, we first discuss the pseudo-perturbation methods. Fermion representation and perturbation renormalization group. Then we study the theoretical scheme of nonperturbed renormalization and the Bethe ansatz rigorous solution method in detail. In Chapter 4th, We find that a weakly coupled Landau Fermi liquid theory can be used to characterize this fixed point in the strongly coupled region. From Chapter 5th to Chapter 8th, I mainly discuss the related research and application of Kondo effect in topological quantum system. Chapter 5th mainly introduces the current research situation in this field. Chapters 6th to 8th are three specific research examples. We can see that although the Kondo effect is a research topic with a history of more than half a century, when it is combined with the new topological state system, it will not only show different physical characteristics from the traditional Kondo effect. It is also possible to produce more novel topological quantum states.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O469

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