拓扑绝缘体及其性质的研究

发布时间：2018-03-29 12:05

本文选题：拓扑绝缘体　切入点：核多项式方法　出处：《东南大学》2016年博士论文

【摘要】：拓扑绝缘体作为一种新的物态,在凝聚态物理,材料科学等方向引起了人们的广泛关注。与普通绝缘体截然不同之处是,拓扑绝缘体拥有拓扑保护且无能隙的边界或表面态,这些边界或表面态不受非磁性杂质和微扰的影响。拓扑绝缘体的拓扑性由Z2不变量来描述。近几年的研究表明拓扑绝缘体会表现出一些奇异的现象,并被认为在自旋电子学以及量子计算机等方向具有很多潜在的应用。本文通过拓扑能带理论,并结合核多项式方法、第一性原理计算,研究了二维、三维拓扑绝缘体的拓扑性质。具体的研究内容和结果包括：1.利用紧束缚近似方法,我们首次指出α-graphyne晶格可以支持拓扑相的存在。通过计算Z2拓扑不变量以及边界态来确定拓扑绝缘体。同时,我们给出了不同填充因子下α-graphyne的相图,该相图是自旋轨道耦合相互作用和最近邻耦合作用的函数。我们发现对于不同的填充因子仅存在两种拓扑相：普通能带绝缘体和拓扑绝缘体,而没有金属相的存在。随后我们分析和讨论了α-graphyne各种拓扑相边界态的特征。2.目前对于石墨烯中安德森无序引起的局域化是否满足单参量标度理论的问题一直争论不休,因而研究无序对同样具有狄拉克结构的graphyne族晶格局域化的影响将是十分有意义的。我们利用紧束缚方法以及变系数核多项式方法,分析了安德森无序对β-graphyne薄片局域化性质的影响。为了区分局域态和扩展态,我们比较了局域态密度的两个特征量：标准态密度pt,以及平均态密度ρme。我们发现不同于石墨烯薄片,β-graphyne态密度的一个鲜明特征是具有很多范霍夫奇点。另外,随着无序强度的增加,从能谱的两侧边界开始,pty逐渐被抑制并在无序强度γ12t时消失,这意味着存在临界无序强度,对于整个能谱是局域化的。同时仅用一个有限尺寸的系统来研究局域化性质是不充分的,需要考虑归一化的标准态密度。通过计算归一化标准态密度,可以得到临界无序强度。发现临界无序强度随着β-graphyne薄片尺寸的增加而减少,当系统无限大时临界无序强度趋近于0。随后我们给出了归一化的标准态密度在能量-无序平面的等高线,从等高线图中可以得到迁移率边界以及里夫希茨边界。最后,为了直观的理解扩展态和局域态的内部结构,我们给出了能带中心(E=0)处的局域态密度。当无序强度增加到γ=12t,团簇被限制为很多独立的岛,这预示着这些状态已经完全局域化,相应的系统由金属转变为绝缘体,即发生了安德森转变。3.利用紧束缚模型我们证明了考虑Rashba自旋轨道耦合作用时正方-八边形晶格也会支持拓扑绝缘体的存在。我们利用整数场方法计算Z2拓扑不变量并给出了不同本征自旋轨道耦合强度和填充因子下的相图。我们发现即使不考虑本征自旋轨道耦合作用,在1/4和3/4填充因子下也会有拓扑绝缘体的存在。而当本征自旋轨道耦合强度合适时(λso=0.4t),不管Rashba自旋轨道耦合作用以及在位势能的强度多么小,在1/4和3/4填充因子下都会出现拓扑绝缘体。同时当填充因子为1/2时,只要0λR,λc1,也会出现拓扑绝缘体。我们分析和讨论了正方-八边形品格的边界态性质。并且通过计算态密度分布以及自旋算符在边界态下的平均值以了解边界态的模式。4.通过将二维正方-八边形晶格进行三维推广,可以得到超立方烷型晶格。通过紧束缚方法以及拓扑能带理论,我们研究超立方烷型晶格在考虑自旋轨道耦合作用时拓扑性质的变化。通过计算Z2拓扑数,我们发现超立方烷型晶格能支持强拓扑绝缘体的存在,同时给出了不同填充因子下的相图。我们发现Z2拓扑数为(1；000)以及(1；111)的强拓扑绝缘体能在1/8填充因子下实现,而在1/8,1/4和1/2填充因子下可得到半金属,在半金属中导带仅在布里渊区中的几个孤立点和价带接触。随后我们分析和讨论了这些拓扑绝缘体以及表面态的特征。而作为拓扑相的一个重要特征,我们也求解了111表面的自旋极化,并且发现自旋极化只位于费米面的平面内,没有分量垂直于平面。同时,对于上狄拉克锥和下狄拉克锥,表面态有相反的赝自旋螺旋性。特别的,下狄拉克锥会随着化学势接近价带的顶端而发生自旋极化的畸变。5.基于第一性原理计算,我们研究了X8(X:C,Si,Ge,Sn,Pb)品格结构以及在静压应变下的拓扑性质。在这些晶格中除了Pb8大部分是动力学稳定的,具有负的结合能且声子谱中没有虚频。由于X8(X=C,Si,Ge,Sn)仅包含轻元素,其自旋轨道耦合强度非常的弱,导致自旋轨道耦合作用对x8(X=C,Si,Ge,Sn)能带结构的影响很小,不会产生拓扑非平庸态。但是除了自旋轨道作用之外,广泛存在于材料表面和界面的应变对半导体或半金属电子性质也有着非常重要的影响,因而我们讨论了静压应变的影响。我们发现对于C8和Si8静压应变不能引起拓扑平庸态和非平庸态之间的量子相变。而对于Ge8和Sn8,拉伸应变能在改变能带拓扑性方面扮演着特殊的角色,即产生Z2不变量为(1；111)的拓扑非平庸态。虽然拓扑相变发生在费米能级以上,但是可以通过施加静电门电压来调节费米能级,更为重要的是,我们的研究表明由轻元素构成的单质也有潜力实现三维拓扑绝缘体。
[Abstract]:Topological insulator as a new material, in condensed matter physics, material science direction has attracted widespread attention. And is very different from the ordinary insulator, topological insulator protection and topology have gapless boundary or surface states, these boundary or surface states is not affected by non magnetic impurities and perturbation of the topology. A topological insulator is described by Z2 invariants. Recent research shows that the topology of insulation exhibit some strange phenomenon, and is believed to have many potential applications in spintronics and quantum computers. The band theory by topology, combined with kernel polynomial method, first principle calculation, study the two-dimensional and the topological properties of three-dimensional topological insulator. The specific research contents and results are as follows: 1. by using the tight binding approximation method, we first pointed out that the -graphyne can support the extension of alpha lattice Flutter phase. Through the calculation of Z2 topological invariants and the boundary state to determine the topological insulator. At the same time, we give the phase diagram of alpha -graphyne under different fill factor, the phase diagram is a function of spin orbit interaction and the nearest neighbor coupling. We find that for different fill factors there are only two kinds of topological phase: General band insulator and topological insulator, and no metal phase. Then we analyze the phase boundary of alpha -graphyne topology state characteristics of.2. for localization of graphene in disorder caused by Anderson do not satisfy the single parameter scaling theory, the problem has been debated and discussed, which also has influence on the Study on the random graphyne lattice the localization of the Dirac structure will be very meaningful. We use the tight binding method and variable coefficient kernel polynomial method, analysis of Anderson Effect of sequence of beta sheet -graphyne localization properties. In order to District branch of localized and extended states, we compared the two features of the local density of states: density Pt standard state, and the average density of P me. we found different from graphene sheets, a distinctive feature of beta -graphyne density is a lot of van hove singularity. In addition, with the increase of the disorder strength, starting from the two boundary spectrum, Pty was gradually suppressed and disappeared in the random strength gamma 12t, which means that there exists a critical disorder strength, for the entire spectrum is localized. At the same time with only a finite size system to study the property is not sufficient, the need to consider the standard density normalized. The normalized standard density, can be obtained. It was found that the critical strength critical disorder disorder strength decreases with the increasing size of the -graphyne beta sheet, when the system is infinite When the critical disorder strength tends to 0. then we give the normalized standard state density in the energy contour disorder plane, contour map can be obtained from the mobility of the boundary and the boundary. Finally, in order to Reeve Hitz, intuitive understanding of extended and localized states of the internal structure, we give the band center (E=0) the local density of states at. When the disorder strength increased to gamma =12t, clusters are restricted to many independent Island, which indicates that the state has been completely localized, the corresponding system is composed of metal to insulator, which happened to Anderson turned.3. by using the tight binding model we show that considering the Rashba spin orbit interaction when Affirmative eight edge shaped lattice will also support topological insulator existence. We use integer field method to calculate Z2 topological invariants and give different intrinsic spin orbit coupling strength and the filling factor Phase diagram. We found that even without considering the intrinsic spin orbit coupling, there will also be a topological insulator in 1/4 and 3/4 under the fill factor exists. When the intensity of the intrinsic spin orbit coupling when appropriate (2 so=0.4t), regardless of the Rashba spin orbit coupling and energy intensity in how small, in the 1/4 and 3/4 fill factor it will be a topological insulator. At the same time when the fill factor is 1/2, as long as 0 x R, lambda C1, will also appear in topological insulators. We analyze and discuss the Affirmative - eight shape character boundary state properties. And by calculating the distribution of the density of States and spin operator in the boundary conditions in order to understand the value of the average.4. boundary state by two-dimensional Affirmative - eight shape 3D lattice extension, can get super cubic type lattice. The tight binding method and topological band theory, we study the super cubic type lattice in consideration of the spin orbit Changes of topological properties of coupling. By calculating the Z2 topology, we found that super cubic type lattice can support strong topological insulators are also given different filling factors. We found that the phase diagram of Z2 topological number (1; 000) and (1; 111) of the insulation can be achieved in the strong topology 1/8 fill factor, and fill in the 1/8,1/4 and 1/2 factor can be obtained in half half metal, metal band only a few isolated points in the Brillouin zone in the valence band and contact. Then we analyze and discuss the characteristics of the topological insulator and surface state. As a topological phase is an important feature, we also solve the spin polarization of the 111 surface, and found only in plane spin polarized Fermi surface, no component perpendicular to the plane. At the same time, the Dirac cone and Dirac cone, a pseudo spin spiral surface states of opposite special, Dirac cone distortion of.5. with top chemical potential and close to the valence band spin polarization based on first principle calculations, we study the X8 (X:C, Si, Ge, Sn, Pb) character structure and topological properties in static strain. In these lattice in addition to most Pb8 is kinetically stable, with negative the binding energy and the phonon spectrum no imaginary frequency. Because X8 (X=C, Si, Ge, Sn) containing only light elements, the spin orbit coupling strength is very weak, leading to the spin orbit coupling effect on X8 (X=C, Si, Ge, Sn) band structure is very small, does not produce non topology in addition to mediocre state. But the spin orbit effect, strain widely exists in the surface and interface of material also has a very important influence on the electronic properties of semiconductor or metal, so we discuss the influence of the hydrostatic strain. We found that for C8 and Si8 static strain can cause flat topology Quantum phase transition between Yong state and non state. Mediocrity and for Ge8 and Sn8, the tensile strain with topology change in energy can play a special role, which is Z2 (1; 111) invariant topological non trivial states. Although the topological transformation occurs at the Fermi level, but can be applied through the static switch the voltage to adjust the Fermi level, more importantly, our study shows that the element consisting of light elements and has the potential to achieve three-dimensional topological insulator.

【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O469

【相似文献】