时间周期驱动下凝聚态系统的拓扑量子态及其输运性质的研究

发布时间：2018-06-28 02:20

本文选题：自旋-轨道耦合 + BHZ模型　；参考：《南京大学》2017年博士论文

【摘要】：时间周期性外场驱动下凝聚态系统的拓扑态以及和其相关的输运现象的研究一直是近几年的热点。本文主要分为两部分,第一部分讨论了二维拓扑绝缘体中的Floquet拓扑相变和自旋极化输运现象；在第二部分,我们提出了二维拓扑绝缘体中的一种绝热拓扑自旋泵浦效应。本文的内容安排如下：第一章中,我们简要介绍了拓扑绝缘体理论的发展以及由拓扑绝缘体衍生出的更为广泛的对称保护拓扑态的概念。在第二章中,我们首先介绍了由拓扑绝缘体的研究发展而来的拓扑能带理论,并利用对称性分析的方法讨论了石墨烯晶格中的自旋轨道耦合项,并由此推导出Kane-Mele模型哈密顿量的二次量子化形式。其次我们用较短的篇幅介绍了BHZ模型的理论和实验。最后,我们用路径积分的方法得到了Keyldsh-Green函数的基本形式,然后借助于这套方法得到了线性响应下电导张量的具体表达式,并证明了零温条件下电导与拓扑不变量之间的关系。在第三章,我们首先给出了Floquet理论的基本框架,并且证明了非共振光极限下的有效哈密顿量的表达式。我们利用这套理论研究了二维平面内时间周期性圆偏振光驱动下的Bernevig-Hughs-Zhang模型,我们发现在非共振光极限下,光场的贡献等价于Zeeman交换场的贡献,并且附带一个修正Dirac质量的项,而且这两个附加项可以被光场的旋转方向和强度所调控。随着光强从零开始增大,我们发现不管系统的初始状态是量子自旋Hall态还是拓扑平庸态,都将经历一次拓扑相变到量子反常Hall态。这提供了一种实验上实现量子反常Hall效应的新方案。通过对纵向电导的计算,我们发现一种可控的自旋极化的输运方案,这为研究拓扑自旋器件提供了新的思路。在第四章,我们提出了一种用自旋陈数刻画的拓扑自旋泵浦效应——自旋陈泵浦效应。不同于第三章的Floquet:方法,我们这里考虑的是绝热近似下的驱动。我们发现每经历一次时间周期,由于系统有着非零的自旋陈数,有数量正比于样品宽度的电子被泵浦到非磁性电极上。此外,我们设计了一套实验方案,利用自旋极化金属导线来测量量子化的电荷泵浦电导,从而实现对系统自旋陈数的测量。这个发现使得我们可以直接利用拓扑绝缘体的稳定拓扑性质。在本文的最后,我们做了一点总结和展望。
[Abstract]:The topological state of condensed state systems driven by time periodic field and the related transport phenomena have been the hot spots in recent years. This paper is divided into two parts. The first part is divided into two parts. The first part discusses the topological and spin polarized transport phenomena in two-dimensional topological insulators; in the second part, we propose a two-dimensional topology. In the first chapter, we briefly introduce the development of topological insulator theory and the more extensive symmetry protection topology derived from topological insulators in Chapter 1. In the second chapter, we first introduce the research and development of topological insulators. The topological energy band theory and the method of symmetry analysis are used to discuss the spin orbit coupling in the graphene lattice and derive the two quantized form of the Hamiltonian of the Kane-Mele model. Secondly, we introduce the theory and experiment of the BHZ model in a shorter length. At the end, we use the path integral method to get the Keylds In the third chapter, we first give the basic framework of the Floquet theory and prove the effective Hamiltonian in the non resonant light limit. We use this theory to study the Bernevig-Hughs-Zhang model driven by the time periodic circular polarized light in two-dimensional plane. We find that the contribution of the light field to the Zeeman exchange field is equivalent to the contribution of the Zeeman exchange field at the non resonant light limit, and it is accompanied by an item that corrections the Dirac mass, and the two additional terms can be used by the light field. As the light intensity increases from zero, we find that whether the initial state of the system is a quantum spin Hall state or a topological mediocre state, we will experience a topological phase transition to a quantum abnormal Hall state. This provides a new scheme for the experimental realization of the quantum anomalous Hall effect. We find a controllable spin polarization transport scheme, which provides a new idea for the study of topological spin devices. In the fourth chapter, we propose a spin Chen Shu pumped effect - spin Chen pump effect. Unlike the third chapter, the Floquet: square method, we consider the adiabatic approximation We find that every time we experience a time period, because the system has a nonzero spin Chen Shu, the electrons with a positive ratio to the width of the sample are pumped to the nonmagnetic electrode. In addition, we have designed a set of experimental schemes to measure the quantized charge pump conductance by using the spin polarized metal wire to realize the system spin Chen Shu. This finding enables us to directly utilize the stable topological properties of topological insulators. At the end of this paper, we make some summaries and prospects.
【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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