拓樸絕緣體是近十年來備受重視之ㄧ新穎量子材料，其塊材能帶的拓樸性質由Z2拓樸不變量所刻劃。拓樸絕緣體具有拓樸表面態，處於表面態的電子的動量與自旋具相互垂直的特性而被稱為「自旋-動量鎖定」。破壞拓樸絕緣體的時間反演對稱性，可以導致許多新奇的物理現象，例如：量子反常霍爾效應。在本工作中，我們結合拓樸絕緣體Bi2Se3與鐵質絕緣體釔鐵石榴石(YIG)、銩鐵石榴石(TmIG)，透過磁鄰近效應來破壞時間反演對稱性，利用此一方法，我們期待在拓樸絕緣體介面誘導出在膜面上均勻的磁化強度，而不會引入晶體缺陷，這是之前以參雜磁性元素的方法所無法達成的。
　　高品質YIG薄膜可藉由室溫離軸濺鍍再加上高溫退火所得，Bi2Se3是由分子束磊晶在280℃成長於YIG表面。我們在Bi2Se3/YIG異質結構中觀察到奇特的負磁阻現象，我們引用弱局域效應疊加在弱反局域效應上可解釋此現象。我們的分析顯示了弱局域效應來自於表面態因介面交換耦合作用，而在狄拉克點打開一個能隙。透過弱局域項與弱反局域項對Bi2Se3厚度的關係顯示出弱局域效應很可能源自於Bi2Se3與YIG的介面; 並且弱局域項是Bi2Se3與YIG之間存在強交換耦合作用的證據。再者，在低溫下電阻與溫度的對數成正比，我們對此一現象做了詳盡分析。κ≡(πh/e^2)∆σ/∆LnT對磁場的關係呈現非單調趨勢，此一趨勢源自弱反局域項與弱局域項有不同的去相干磁場。
　　交換耦合能隙取決於磁化的垂直分量，為確保在沒有外加磁場的情況下，拓樸表面態能夠打開能隙，我們將鐵磁絕緣體由YIG換成TmIG，TmIG是一種最近被發現具垂直磁異向性與方形磁滯曲線的新材料。除了亦觀察到負磁阻之外，我們藉由改變外加磁場與薄膜的夾角，觀察到當磁場與薄膜的夾角縮小後，負磁阻隨之減弱的現象。此一現象能夠用磁化強度單位向量在垂直方向的分量減小來解釋，垂直方向的分量減小會導致拓樸表態面的能隙變小。我們並且進行了兩個額外量測，即反常霍爾性應與異向磁阻，來探測Bi2Se3中的磁化。觀察到反常霍爾效應顯示Bi2Se3透過磁鄰近效應誘導出磁性。異向磁阻的振幅對磁場呈線性關係且截距為正，此一趨勢可能與磁鄰近效誘導出的磁性有密切的關係。
　　總結，我們成功地結合了Bi2Se3薄膜與YIG、TmIG薄膜。低溫磁傳輸量測驗證弱局域效應、反常霍爾效應與異向磁阻的存在，顯示了拓樸絕緣體與鐵磁絕緣體之間存在相當強的交換耦合效應。使用TmIG作為鐵磁絕緣體能夠確保在沒有外加磁場下，拓樸表面態可打開了能隙。可望此前瞻研究有助於在更高的溫度下實現量子反常霍爾效應，以及在未來發展量子計算與自旋電子學等相關應用。

Topological insulators (TIs) are quantum materials characterized by their nontrivial topology Z2 of gapped bulk band structures. They exhibit topological surface states (TSSs) with spin momentum locking. Breaking time reversal symmetry (TRS) of TSSs leads to novel phenomena such as quantum anomalous Hall effect (QAHE). In this work we integrated the topological insulator Bi2Se3 with magnetic insulators yttrium iron garnet (YIG) and thulium iron garnet (TmIG) to break TRS through a novel mechanism: magnetic proximity effect (MPE) that enables the generation of uniform magnetization in the film plane without introducing crystal defects, as opposed to the previous method of adding magnetic dopants like Cr into TI.
High quality YIG thin films were grown by off-axis sputtering at room temperature followed by high temperature anneals and Bi2Se3 thin films were deposited at 280℃ by MBE. It was observed that, in contrast to Bi2Se3/Sapphire, the distinctive negative magnetoresistance (MR) observed in Bi2Se3/YIG was attributed to emerging weak localization (WL) component superimposed on known weak antilocalization (WAL) component. Our analysis indicates that the WL component in Bi2Se3/YIG resulted from a gap opened at the Dirac point due to the interfacial exchange coupling. The dependence of the WL and WAL components on the Bi2Se3 thickness implies that the WL component is originated from the interface of Bi2Se3 and YIG. The logarithmic temperature dependence of the resistance was also analyzed. κ≡(πh/e^2)∆σ/∆LnT shows the non-monotonic field dependence, resulting from different dephasing fields of WAL and WL. A WL component manifesting as the negative MR and logarithmic increasing in RT curves provide strong evidences for strong exchange-coupling interaction between Bi2Se3 and YIG.
An exchange-coupling gap depends on the normal component of the magnetization. To ensure a finite gap opening without the external field, we replaced the magnetic insulators from YIG with in-plane magnetic anisotropy (IMA) to TmIG with perpendicular magnetic anisotropy (PMA) and square-shaped hysteresis loops. High quality TmIG thin films were grown by off-axis sputtering. We also observed the negative MR in Bi2Se3/TmIG. In addition, the negative MR weakened when the magnetization was aligned toward the in-plane direction, which can be understood in the picture of reduced gap size due to the decreased out-of-plane component of the magnetization. Two additional measurements, the anomalous Hall effect (AHE) and the anisotropic MR (AMR), were carried out to probe the induced magnetization in Bi2Se3. The observations of AHE indicates the ferromagnetism is developed in Bi2Se3 via MPE. The amplitude of AMR shows a linear field dependence with a positive intercept, which may be closely related the proximity-induced ferromagnetism.
In summary, we have successfully integrated Bi2Se3 thin films with YIG or TmIG thin films to form high quality TI/MI heterostructures with abrupt interfaces. Comprehensive low temperature magneto-transport studies have observed the salient features identifiable as WL, AHE and AMR, providing strong evidences for strong interfacial exchange coupling between Bi2Se3 and YIG or TmIG. The utilization of TmIG of PMA ensures a finite gap opened up without external field. Our study may pave the way to realize QAHE at higher temperatures, thus viable for quantum computing or spintronic applications in future.

Abstract i
摘要 iv
Acknowledgement vi
Content vii
List of figures ix
List of tables xii
Chapter 1 Introduction 1
1.1 Introduction of topological insulator 1
1.1.1 TKNN invariant 1
1.1.2 Edge states and the bulk-boundary correspondence 3
1.1.3 Two dimensional and three dimensional topological insulators 4
1.2 Time reversal symmetry (TRS) breaking in TI 6
1.3 Methods of breaking TRS 7
1.3.1 Transition metal doping 7
1.3.2 Magnetic proximity effect 9
1.4 Ordinary Hall effect and anomalous Hall effect 12
1.4.1 Ordinary Hall effect 12
1.4.2 Anomalous Hall effect 13
1.5 Motivation of this work 14
Chapter 2 Experimental procedures 16
2.1 Deposition of magnetic insulator thin films 16
2.1.1 Introduction of sputter 16
2.1.2 Thin film deposition of yttrium iron garnet (YIG) 18
2.1.3 Thin film deposition of thulium iron garnet (TmIG) 19
2.2 Deposition of topological insulator thin films on magnetic insulator 21
2.2.1 Introduction of molecular beam epitaxy 21
2.2.2 Thin film deposition of Bi2Se3 on YIG 22
2.2.3 Thin film deposition of Bi2Se3 on TmIG 23
2.3 Hall bar fabrication 23
2.4 Transport properties measurement 25
2.4.1 Introduction of Physical Properties Measurement System 25
2.4.2 Four point measurement 27
2.4.3 Angular dependence measurement 28
Chapter 3 Transport properties of Bi2Se3/YIG 29
3.1 Characterization 29
3.1.1 Structural analysis by RHEED, XRD, TEM and AFM 29
3.1.2 Thickness dependence of transport properties 31
3.2 Quantum interference effect 32
3.2.1 Introduction of weak antilocalization and weak localization 32
3.2.2 Theory 34
3.2.3 Analysis of experimental results 36
3.3 Resistance-Temperature (RT) curve analysis 43
Chapter 4 Transport properties of Bi2Se3/TmIG 49
4.1 Motivation of changing magnetic insulator from YIG to TmIG 49
4.2 Characterization 49
4.2.1 Structural analysis by RHEED, XRD, and AFM 49
4.3 Quantum interference effect 51
4.4 Magnetoresistance at various angles 52
4.5 Observation of anomalous Hall effect (AHE) and anisotropic magnetoresistance (AMR) 55
4.3.1 Observation of AHE 55
4.3.2 Observation of AMR 57
Chapter 5 Summary 60
Reference 61

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