安德森拓扑绝缘体的输运性质研究

发布时间：2018-10-20 07:44

【摘要】：二维拓扑绝缘体又称为自旋量子霍尔绝缘体(QSH),于2005-2006年间被理论预言后,2007在碲化汞、碲化镉量子阱的实验中观测到。这个进展是拓扑绝缘体理论和材料发展的重要里程碑,而整个拓扑绝缘体领域构成了当代凝聚态物理的新篇章。过去近十年,关于拓扑绝缘体的研究已经取得了显著的成果。其中一个分支,是人们重新研究了无序对电子结构的影响,发现无序可以对体系的拓扑性质发生根本性的影响。人们发现在拓扑平庸的材料中,可以通过引入无序作用诱导拓扑安德森相变,导致拓扑绝缘体。在所谓的拓扑安德森绝缘态,体内电子都发生安德森局域化,但是在体系边界存在受拓扑保护的边缘态。除了无序度以外,安德森拓扑绝缘体的输运性质还受到系统中其他参数的影响,比如系统的尺度、费米能量、质量参数等。本文主要研究系统的尺度是如何影响金属绝缘相变的问题,前人已经研究出在一定安德森无序下体系中出现的量子化电导会随着系统尺度的减小而消失。我们的工作是对前人关于安德森相变中的尺度效应做进一步延伸。本文从二维拓扑绝缘体材料中的碲化汞/碲化镉量子阱出发,运用递归非平衡格林函数法计算其输运性质。对比不同尺度下系统的输运性质,通过对相图的分析,发现在小尺度的系统中,量子化电导区域并不像大尺度体系那样是一块连续的区域,而是几块分离的区域。随着尺度的增大,分离的量子化电导区域才倾向性地连成一块区域。尺度的限制使系统的能带区别于拓扑非平庸绝缘体。进一步研究发现,小尺度下在狄拉克点打开的能隙宽度大于理论上的2|M|,随着系统尺度的增大,系统的能隙才会逐渐趋于这个理论值,这个结论很好地解释了前人发现的量子化电导随尺度的减小而消失的现象：量子化电导并不是真的消失了,而是由于能隙宽度的增大,它的位置也随之发生改变。研究中作者针对相图里各种区域中出现的现象做出了比较合理的解释,发现一些有趣的变化,原本很小的安德森量子化电导区域会随着尺度的增大而增大。此外还讨论了关联性对输运性质的影响,发现关联性的加入会正重整化拓扑质量,并降低系统的稳定性。
[Abstract]:Two dimensional topological insulators, also known as spin quantum Hall insulators (QSH), were predicted in theory in 2005-2006, and 2007 were observed in experiments of HgTe and CdTe quantum wells. This development is an important milestone in the development of topological insulator theory and materials, and the whole field of topological insulators constitutes a new chapter in contemporary condensed matter physics. In the past ten years, remarkable achievements have been made in the study of topological insulators. One of the branches is the restudy of the influence of disorder on the electronic structure. It is found that disorder can have a fundamental effect on the topological properties of the system. It has been found that topological insulators can be induced by the introduction of disorder in the mediocre topological materials. In the so-called topological Anderson insulating state, the electrons in the body occur Anderson localization, but at the boundary of the system there exists the edge state which is protected by topology. In addition to the degree of disorder the transport properties of Anderson topological insulators are also affected by other parameters such as system scale Fermi energy mass parameters and so on. In this paper, we mainly study how the scale of the system affects the phase transition of metal insulation. It has been studied that the quantized conductance in a certain Anderson disorder system will disappear with the decrease of the system scale. Our work is to extend the scale effect of Anderson phase transition. In this paper, the transport properties of mercury telluride / cadmium telluride quantum wells in two dimensional topological insulators are calculated by using the recursive nonequilibrium Green's function method. By comparing the transport properties of the system at different scales and analyzing the phase diagram, it is found that the quantized conductance region is not a continuous region, but several separate regions in a small scale system, as in a large scale system. As the scale increases, the separated quantized conductance regions tend to form a single area. The limitation of scale distinguishes the energy band of the system from the topological nonmediocre insulator. Further study shows that the width of the energy gap opened at the Dirac point is larger than that of the theoretical gap at the small scale. With the increase of the scale of the system, the energy gap of the system will gradually tend to this theoretical value. This conclusion explains the phenomenon that the quantized conductance disappears with the decrease of the scale: the quantized conductance does not really disappear, but the position of the quantum conductance changes with the increase of the gap width. In this study, the author gives a reasonable explanation for the phenomena in various regions of the phase diagram, and finds some interesting changes. The small Anderson quantized conductance region increases with the increase of the scale. In addition, the influence of correlation on transport properties is discussed. It is found that the addition of correlation will positively renormalize the topological quality and reduce the stability of the system.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O471.1

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