本文選題：自旋-軌道耦合 + BHZ模型�。� 參考：《南京大學》2017年博士論文

【摘要】：時間周期性外場驅(qū)動下凝聚態(tài)系統(tǒng)的拓撲態(tài)以及和其相關的輸運現(xiàn)象的研究一直是近幾年的熱點。本文主要分為兩部分,第一部分討論了二維拓撲絕緣體中的Floquet拓撲相變和自旋極化輸運現(xiàn)象；在第二部分,我們提出了二維拓撲絕緣體中的一種絕熱拓撲自旋泵浦效應。本文的內(nèi)容安排如下：第一章中,我們簡要介紹了拓撲絕緣體理論的發(fā)展以及由拓撲絕緣體衍生出的更為廣泛的對稱保護拓撲態(tài)的概念。在第二章中,我們首先介紹了由拓撲絕緣體的研究發(fā)展而來的拓撲能帶理論,并利用對稱性分析的方法討論了石墨烯晶格中的自旋軌道耦合項,并由此推導出Kane-Mele模型哈密頓量的二次量子化形式。其次我們用較短的篇幅介紹了BHZ模型的理論和實驗。最后,我們用路徑積分的方法得到了Keyldsh-Green函數(shù)的基本形式,然后借助于這套方法得到了線性響應下電導張量的具體表達式,并證明了零溫條件下電導與拓撲不變量之間的關系。在第三章,我們首先給出了Floquet理論的基本框架,并且證明了非共振光極限下的有效哈密頓量的表達式。我們利用這套理論研究了二維平面內(nèi)時間周期性圓偏振光驅(qū)動下的Bernevig-Hughs-Zhang模型,我們發(fā)現(xiàn)在非共振光極限下,光場的貢獻等價于Zeeman交換場的貢獻,并且附帶一個修正Dirac質(zhì)量的項,而且這兩個附加項可以被光場的旋轉(zhuǎn)方向和強度所調(diào)控。隨著光強從零開始增大,我們發(fā)現(xiàn)不管系統(tǒng)的初始狀態(tài)是量子自旋Hall態(tài)還是拓撲平庸態(tài),都將經(jīng)歷一次拓撲相變到量子反常Hall態(tài)。這提供了一種實驗上實現(xiàn)量子反常Hall效應的新方案。通過對縱向電導的計算,我們發(fā)現(xiàn)一種可控的自旋極化的輸運方案,這為研究拓撲自旋器件提供了新的思路。在第四章,我們提出了一種用自旋陳數(shù)刻畫的拓撲自旋泵浦效應——自旋陳泵浦效應。不同于第三章的Floquet:方法,我們這里考慮的是絕熱近似下的驅(qū)動。我們發(fā)現(xiàn)每經(jīng)歷一次時間周期,由于系統(tǒng)有著非零的自旋陳數(shù),有數(shù)量正比于樣品寬度的電子被泵浦到非磁性電極上。此外,我們設計了一套實驗方案,利用自旋極化金屬導線來測量量子化的電荷泵浦電導,從而實現(xiàn)對系統(tǒng)自旋陳數(shù)的測量。這個發(fā)現(xiàn)使得我們可以直接利用拓撲絕緣體的穩(wěn)定拓撲性質(zhì)。在本文的最后,我們做了一點總結和展望。
[Abstract]:The topological state of condensed state systems driven by time periodic field and the related transport phenomena have been the hot spots in recent years. This paper is divided into two parts. The first part is divided into two parts. The first part discusses the topological and spin polarized transport phenomena in two-dimensional topological insulators; in the second part, we propose a two-dimensional topology. In the first chapter, we briefly introduce the development of topological insulator theory and the more extensive symmetry protection topology derived from topological insulators in Chapter 1. In the second chapter, we first introduce the research and development of topological insulators. The topological energy band theory and the method of symmetry analysis are used to discuss the spin orbit coupling in the graphene lattice and derive the two quantized form of the Hamiltonian of the Kane-Mele model. Secondly, we introduce the theory and experiment of the BHZ model in a shorter length. At the end, we use the path integral method to get the Keylds In the third chapter, we first give the basic framework of the Floquet theory and prove the effective Hamiltonian in the non resonant light limit. We use this theory to study the Bernevig-Hughs-Zhang model driven by the time periodic circular polarized light in two-dimensional plane. We find that the contribution of the light field to the Zeeman exchange field is equivalent to the contribution of the Zeeman exchange field at the non resonant light limit, and it is accompanied by an item that corrections the Dirac mass, and the two additional terms can be used by the light field. As the light intensity increases from zero, we find that whether the initial state of the system is a quantum spin Hall state or a topological mediocre state, we will experience a topological phase transition to a quantum abnormal Hall state. This provides a new scheme for the experimental realization of the quantum anomalous Hall effect. We find a controllable spin polarization transport scheme, which provides a new idea for the study of topological spin devices. In the fourth chapter, we propose a spin Chen Shu pumped effect - spin Chen pump effect. Unlike the third chapter, the Floquet: square method, we consider the adiabatic approximation We find that every time we experience a time period, because the system has a nonzero spin Chen Shu, the electrons with a positive ratio to the width of the sample are pumped to the nonmagnetic electrode. In addition, we have designed a set of experimental schemes to measure the quantized charge pump conductance by using the spin polarized metal wire to realize the system spin Chen Shu. This finding enables us to directly utilize the stable topological properties of topological insulators. At the end of this paper, we make some summaries and prospects.
【學位授予單位】：南京大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：O469

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