【作者】 孙亮；

【导师】 完绍龙；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2014， 博士

【摘要】 近年来拓扑绝缘体、Weyl semimetal等一系列拓扑非平凡的物态是凝聚态物理研究的热点,对拓扑绝缘体以及Weyl semimetal的研究大大地加深了人们对凝聚态物理的理解,揭示了凝聚态物理与高能物理的联系。这篇博士论文除了介绍拓扑绝缘体、Weyl semimetal的基本物理外,主要包含以下几方面内容：(1)我们研究了由于周期势的引入使得体内能带陈数(TKNN不变量)分裂的物理,揭示了原来能带的陈数与分裂后子能带的陈数之间的关系。在此之前,人们只知道子能带的陈数之和必然等于原来的陈数,却不能精确的知道具体每一个子能带的陈数。在这项工作中,我们发现对于最一般的情况,任意一能带被分裂成两个能带的情形,子能带的陈数不仅与原来能带的陈数相关,还由周期势的相位因子绕着新的布里渊区的环路积分决定。(2)论文系统的介绍了Weyl semimetal这一拓扑非平凡的半金属的实验与理论研究背景,以及一些基本的物理性质。Weyl semimetal是一种三维拓扑非平凡的半金属。其体内有偶数个在动量能量空间中分开的、带有手征性的Weyl点,在每一个Weyl点上,Berry curvature变成奇点,类似于动量空间磁单极。Weyl semimetal有着无能隙的表面态,且连接于体内的Weyl点。电场在Weyl semimetal中会产生反常霍尔效应AHE,而磁场却可以产生不寻常的手征磁效应CME,这两种效应都可以从其电磁响应的有效作用量中而得到。(3)弹性响应,与电磁响应类似,也是一种可以用来体现拓扑非平凡物理的响应。论文中我们研究了三维Weyl semimetal中的反常弹性响应。我们通过应用Fujikawa手征反常中路径积分的方法得到带有θ项与NY项的有效作用量,并且发现Weyl semimetal材料中存在由位错dislocations而导致的反常动量流,并讨论其物理意义及其应用。(4)论文中,我们首次通过精确对角化的方法,在一般的Weyl semimetal格点模型中,发现手征磁效应所预言的反常电流,其由磁场引起且与磁场的方向相同。我们验证这种反常电流不会随着体系温度、尺寸、化学势的改变而消失,是一种拓扑效应。我们证明了在零温极限下,只有费米面上的电子才对电流有贡献。在外磁场很弱的情况下,我们发现反常电流跟磁场强度、△E有着严格的正比关系,且比例系数为e2/h2,与线性响应理论得到的结果完全一致。在此基础上,我们对存在的原因与理论基础进行了分析与讨论。更多还原

【Abstract】 Recently topological insulators and Weyl semimetals, which have topological non-trivial momentum space topology have attracted considerable attention in condensed matter physics. The research on topological insulators and Weyl semimetals has been deepening our understanding of nature and the relation between condensed matter physics and high energy physics. In this thesis, after an introduction of basic physics on topo-logical insulators and Weyl semimetal, we shall focus mainly on the following topics:(1) We studied the project the periodic potential inducing the splitting of topolog-ical invariant-Chern number for bands in the condensed matter system. We found the relationship between Chern number of original bands and ones from new bands by the periodic potential. People always know the sum of their Chern numbers is equal to the original Chern number, but the exact number for each splitting band is unknown. In this thesis, we found that, in most general case one band is split two bands, the integral of the phase of the periodic potential around the new Brillouin zone also determines the values of new Chern numbers besides the original Chern number.(2) In this thesis, we introduce some basic theoretical results and experiments in this three dimensional nontrivial topological semimetal-Weyl semimetal. There are even numbers Weyl points separated in momentum and energy space in the bulk of Weyl semimetal. Each Weyl points can be viewed as a momentum monopole. There is gap-less surface states connecting the Weyl nodes in the bulk. The electric field can induce the anomalous Hall current in Weyl semimetal because of the separation of Weyl points in momentum space. But most amazing effect is the chiral magnetic effect (CME). The CME said that, even absence the electric field, the charge current can be induced directly by the external magnetic field with the same direction. These effects can be derived from the effective action after coupling to the electromagnetic field.(3) The elastic response can also be calculated to show the topological nontrivial physics just as the electromagnetic response. We studied the anomalous elastic response in three dimensional Weyl semimetal. We get the effective action, which including θ term and NY invariant, adapting the method by Fujikawa in chiral anomaly. We also found that there is the anomalous momentum current in Weyl semimetal induced by the dislocations as Burgers vector. And the physical meaning for this current and its application in condensed matter has also been discussed.(4) Based on the numerical results by the exact numerical diagonalization method, we first demonstrate the existence of the chiral magnetic effect in a general model of Weyl semimetal. As predicted by CME, there is the anomalous current induced by mag- netic field in the same direction. We have evaluated this current for various system sizes, magnetic field strengths, temperatures and the energy difference AE between different Weyl points. The current can be zero only when the energy difference AE=0. We also proved that only the states at the Fermi surface can contribute the current in the zero temperature limit. In the weak field limit, the anomalous current from the numerical result is proportional to the strength of magnetic field and the energy separation with a universal coefficient e2/h2, predicted in the theoretical work. We also discussed the reason of existence for this nontrivial current and its fundamental physics.更多还原