本文選題：拓?fù)浣^緣體　切入點：核多項式方法　出處：《東南大學(xué)》2016年博士論文

【摘要】：拓?fù)浣^緣體作為一種新的物態(tài),在凝聚態(tài)物理,材料科學(xué)等方向引起了人們的廣泛關(guān)注。與普通絕緣體截然不同之處是,拓?fù)浣^緣體擁有拓?fù)浔Ｗo(hù)且無能隙的邊界或表面態(tài),這些邊界或表面態(tài)不受非磁性雜質(zhì)和微擾的影響。拓?fù)浣^緣體的拓?fù)湫杂蒢2不變量來描述。近幾年的研究表明拓?fù)浣^緣體會表現(xiàn)出一些奇異的現(xiàn)象,并被認(rèn)為在自旋電子學(xué)以及量子計算機(jī)等方向具有很多潛在的應(yīng)用。本文通過拓?fù)淠軒Ю碚?并結(jié)合核多項式方法、第一性原理計算,研究了二維、三維拓?fù)浣^緣體的拓?fù)湫再|(zhì)。具體的研究內(nèi)容和結(jié)果包括：1.利用緊束縛近似方法,我們首次指出α-graphyne晶格可以支持拓?fù)湎嗟拇嬖凇Ｍㄟ^計算Z2拓?fù)洳蛔兞恳约斑吔鐟B(tài)來確定拓?fù)浣^緣體。同時,我們給出了不同填充因子下α-graphyne的相圖,該相圖是自旋軌道耦合相互作用和最近鄰耦合作用的函數(shù)。我們發(fā)現(xiàn)對于不同的填充因子僅存在兩種拓?fù)湎啵浩胀軒Ы^緣體和拓?fù)浣^緣體,而沒有金屬相的存在。隨后我們分析和討論了α-graphyne各種拓?fù)湎噙吔鐟B(tài)的特征。2.目前對于石墨烯中安德森無序引起的局域化是否滿足單參量標(biāo)度理論的問題一直爭論不休,因而研究無序?qū)ν瑯泳哂械依私Y(jié)構(gòu)的graphyne族晶格局域化的影響將是十分有意義的。我們利用緊束縛方法以及變系數(shù)核多項式方法,分析了安德森無序?qū)Ζ?graphyne薄片局域化性質(zhì)的影響。為了區(qū)分局域態(tài)和擴(kuò)展態(tài),我們比較了局域態(tài)密度的兩個特征量：標(biāo)準(zhǔn)態(tài)密度pt,以及平均態(tài)密度ρme。我們發(fā)現(xiàn)不同于石墨烯薄片,β-graphyne態(tài)密度的一個鮮明特征是具有很多范霍夫奇點。另外,隨著無序強(qiáng)度的增加,從能譜的兩側(cè)邊界開始,pty逐漸被抑制并在無序強(qiáng)度γ12t時消失,這意味著存在臨界無序強(qiáng)度,對于整個能譜是局域化的。同時僅用一個有限尺寸的系統(tǒng)來研究局域化性質(zhì)是不充分的,需要考慮歸一化的標(biāo)準(zhǔn)態(tài)密度。通過計算歸一化標(biāo)準(zhǔn)態(tài)密度,可以得到臨界無序強(qiáng)度。發(fā)現(xiàn)臨界無序強(qiáng)度隨著β-graphyne薄片尺寸的增加而減少,當(dāng)系統(tǒng)無限大時臨界無序強(qiáng)度趨近于0。隨后我們給出了歸一化的標(biāo)準(zhǔn)態(tài)密度在能量-無序平面的等高線,從等高線圖中可以得到遷移率邊界以及里夫希茨邊界。最后,為了直觀的理解擴(kuò)展態(tài)和局域態(tài)的內(nèi)部結(jié)構(gòu),我們給出了能帶中心(E=0)處的局域態(tài)密度。當(dāng)無序強(qiáng)度增加到γ=12t,團(tuán)簇被限制為很多獨(dú)立的島,這預(yù)示著這些狀態(tài)已經(jīng)完全局域化,相應(yīng)的系統(tǒng)由金屬轉(zhuǎn)變?yōu)榻^緣體,即發(fā)生了安德森轉(zhuǎn)變。3.利用緊束縛模型我們證明了考慮Rashba自旋軌道耦合作用時正方-八邊形晶格也會支持拓?fù)浣^緣體的存在。我們利用整數(shù)場方法計算Z2拓?fù)洳蛔兞坎⒔o出了不同本征自旋軌道耦合強(qiáng)度和填充因子下的相圖。我們發(fā)現(xiàn)即使不考慮本征自旋軌道耦合作用,在1/4和3/4填充因子下也會有拓?fù)浣^緣體的存在。而當(dāng)本征自旋軌道耦合強(qiáng)度合適時(λso=0.4t),不管Rashba自旋軌道耦合作用以及在位勢能的強(qiáng)度多么小,在1/4和3/4填充因子下都會出現(xiàn)拓?fù)浣^緣體。同時當(dāng)填充因子為1/2時,只要0λR,λc1,也會出現(xiàn)拓?fù)浣^緣體。我們分析和討論了正方-八邊形品格的邊界態(tài)性質(zhì)。并且通過計算態(tài)密度分布以及自旋算符在邊界態(tài)下的平均值以了解邊界態(tài)的模式。4.通過將二維正方-八邊形晶格進(jìn)行三維推廣,可以得到超立方烷型晶格。通過緊束縛方法以及拓?fù)淠軒Ю碚?我們研究超立方烷型晶格在考慮自旋軌道耦合作用時拓?fù)湫再|(zhì)的變化。通過計算Z2拓?fù)鋽?shù),我們發(fā)現(xiàn)超立方烷型晶格能支持強(qiáng)拓?fù)浣^緣體的存在,同時給出了不同填充因子下的相圖。我們發(fā)現(xiàn)Z2拓?fù)鋽?shù)為(1；000)以及(1；111)的強(qiáng)拓?fù)浣^緣體能在1/8填充因子下實現(xiàn),而在1/8,1/4和1/2填充因子下可得到半金屬,在半金屬中導(dǎo)帶僅在布里淵區(qū)中的幾個孤立點和價帶接觸。隨后我們分析和討論了這些拓?fù)浣^緣體以及表面態(tài)的特征。而作為拓?fù)湎嗟囊粋�重要特征,我們也求解了111表面的自旋極化,并且發(fā)現(xiàn)自旋極化只位于費(fèi)米面的平面內(nèi),沒有分量垂直于平面。同時,對于上狄拉克錐和下狄拉克錐,表面態(tài)有相反的贗自旋螺旋性。特別的,下狄拉克錐會隨著化學(xué)勢接近價帶的頂端而發(fā)生自旋極化的畸變。5.基于第一性原理計算,我們研究了X8(X:C,Si,Ge,Sn,Pb)品格結(jié)構(gòu)以及在靜壓應(yīng)變下的拓?fù)湫再|(zhì)。在這些晶格中除了Pb8大部分是動力學(xué)穩(wěn)定的,具有負(fù)的結(jié)合能且聲子譜中沒有虛頻。由于X8(X=C,Si,Ge,Sn)僅包含輕元素,其自旋軌道耦合強(qiáng)度非常的弱,導(dǎo)致自旋軌道耦合作用對x8(X=C,Si,Ge,Sn)能帶結(jié)構(gòu)的影響很小,不會產(chǎn)生拓?fù)浞瞧接箲B(tài)。但是除了自旋軌道作用之外,廣泛存在于材料表面和界面的應(yīng)變對半導(dǎo)體或半金屬電子性質(zhì)也有著非常重要的影響,因而我們討論了靜壓應(yīng)變的影響。我們發(fā)現(xiàn)對于C8和Si8靜壓應(yīng)變不能引起拓?fù)淦接箲B(tài)和非平庸態(tài)之間的量子相變。而對于Ge8和Sn8,拉伸應(yīng)變能在改變能帶拓?fù)湫苑矫姘缪葜厥獾慕巧?即產(chǎn)生Z2不變量為(1；111)的拓?fù)浞瞧接箲B(tài)。雖然拓?fù)湎嘧儼l(fā)生在費(fèi)米能級以上,但是可以通過施加靜電門電壓來調(diào)節(jié)費(fèi)米能級,更為重要的是,我們的研究表明由輕元素構(gòu)成的單質(zhì)也有潛力實現(xiàn)三維拓?fù)浣^緣體。
[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.

【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O469

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