兰州大学机构库 >物理科学与技术学院
周期性驱动系统中极端拓扑相的研究
Alternative TitleTowards Extremal Topological Phases in Periodically Driven Systems
熊天时
Thesis Advisor安钧鸿
2016-05-30
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword大陈数 拓扑绝缘体 狄拉克锥
Abstract拓扑绝缘体是基于拓扑序划分的一类拥有绝缘内部块体和导电边界的材料,它能够在没有对称性破缺的情况下实现量子霍尔效应。这些奇异的导电特性来源于其特有的无能隙的边缘态。拓扑绝缘体中边缘态的数目取决于其动量空间中能带结构的拓扑性质。因为材料的拓扑性质对于材料参数的连续变化并不敏感,所以拓扑绝缘体的物理特性(如霍尔电导和边缘态数目)较为稳定。此外拓扑绝缘体还与Majorana费米子、Weyl半金属、量子计算等领域紧密相关,这使之成为了近些年来凝聚态领域的热门问题。 拓扑绝缘体的拓扑性质由相应的拓扑不变量刻画。因为二维系统的拓扑不变量为陈数,所以由陈数刻画的拓扑绝缘体也被称为陈绝缘体。实验上实现的陈绝缘体相应的陈数仅为1,在许多应用领域中以大陈数拓扑相为代表的极端拓扑物态具有不可替代的作用,因此如何产生该极端拓扑物态受到了广泛关注。理论揭示在多层结构与长程相互作用的材料中可实现大陈数拓扑绝缘体,但是这些条件在实验上难以实现。 在本文,我们提出利用周期性驱动方案在多层结构与长程相互作用不具备的材料中来实现大陈数极端拓扑物态,以期揭示周期性驱动这一有效的量子调控方案在人工合成拓扑物态中的应用前景。首先,我们基于Floquet理论解析建立了周期性驱动两能带系统拓扑相变的理论,包含相变临界方程及相变规律。基于我们提出了潜在狄拉克点理论,我们揭示了正是周期性驱动所特有的对多重狄拉克锥的产生与调控机制才使得大陈数拓扑绝缘相得以实现。其次,我们以N3 Haldane模型为例具体研究其在周期性驱动下的拓扑相变,我们发现不同于陈数最大为2的静态N3 Haldane模型,周期性驱动的引入将使陈数最大可至7,并依据我们的解析理论对该系统丰富拓扑相图进行分析,分析研究结果证实了我们所提出的解析理论。 我们的工作不仅从理论上证实了周期性驱动能够实现大范围的拓扑非平庸物态的陈数可控调节,而且为有效地解决相关实验通过材料制备来实现极端拓扑物态的困难提供新的思路。
Other AbstractTopological insulators are materials possessing insulating bulks and conductive boundaries, which are classified with the notion of topological order. They are capable to realise the quantum Hall effect with no symmetries broken. All these peculiar properties come from the topological insulators' gapless edge states, whose numbers are determined by the topology of the bands. Because the topology is insensitive to smooth changes in material parameters, the physical properties (such as Hall conductance and the number of gapless boundary modes) are relatively stable. In addition to quantum Hall effects, topological insulators are also closely related to the fields such as Majorana fermions, Weyl semimetals and quantum computaion, which makes it a hot topic in recent years. The topology of topological insulators is characterised by corresponding topological invariant. Because the topological invariant of two dimensional systems is the Chern number, they are also called the Chern insulators. Although extremal topological phases such as large-Chern-number phases is proved to be indispensable in many fields, the experimentally realized Chern numbers are only 1. Theory shows that the realisation of large-Chern-number phases requires long-range interactions or multi-layered structures in materials, which are difficult to realise. We engage in the exploration of extremal topological phases in the periodically driven systems where long-range interactions and multi-layered structures are both absent. Basing on the Floquet theory, we analytically establish the theory of the phase transitions induced by periodic driving in two-band systems. Our theory shows the criteria and the rules of phase transitions. In the theory, we reveal the mechanism of generating and engineering multiple Dirac cones in periodic driven systems which makes the large-Chern-number phases possible. Then we apply the periodic driving to the N3 Haldane model to study the topological phase transitions. After inducing the periodic driving, we obtain the large Chern numbers 7 in the N3 Haldane model, which only has Chern numbers 2 at most in static case. We also analysis the topological phase diagram and check our analytic theory numerically. Our work not only show that the diverse topological phases with a widely tunable Chern numbers can be induced by periodic driving, but also greatly relaxes the experimental difficulty in material fabrication, and opens an avenue to generate extremal topologica...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/229002
Collection物理科学与技术学院
Recommended Citation
GB/T 7714
熊天时. 周期性驱动系统中极端拓扑相的研究[D]. 兰州. 兰州大学,2016.
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