拓樸絕緣體為一種新穎量子物質，由於其特殊的物理性質像是由時間反轉對稱保護的表面態，使科學界在近年來對它有極大的興趣。除此之外，預期在低損耗元件和量子計算上將有重大的應用。
此論文中主要研究藉由分子束磊晶方式成長拓樸絕緣體之樣品性質，藉由凡德瓦力,我們成功長出高品質的硒化铋薄膜在不同的基板上。對於硒化铋的薄膜在不同的基板上，我們的角解析電子能譜中都可以觀察到明顯的表面態跟狄拉克錐。然而，由於內在缺陷，硒化铋的費米能階總是落於導帶裡，這會讓導帶中的電子也會對傳輸造成貢獻。
此外．我們報導，相對一般使用的非結晶硒保護層，用一種新的成長方式成長出的結晶硒保護層，在真空或是大氣環境底下，可以擁有比較好的穩定性跟抗氧化能力。更進一步，時間相關的霍爾效應，指出結晶的硒保護層有比較好的能力，去維持硒化铋的傳輸性質。
為了讓傳輸由表面態主導，我們尋找一種元素態的拓樸絕緣體。錫薄膜擁有許多優點: 由於元素的自然狀態，它不會有像化合物的拓樸絕緣體相關的缺陷。它可以提供不同能帶結構的晶體結構，使我們可以擁有三維到二維的拓樸絕緣體。
我們成功的在碲化铋上長出像是錫烯結構的單層錫。藉由角解析電子能譜，錫烯的電子結構可以被決定。在倒空間原點附近，錫烯的電動帶跟一個由於錫烯跟碲化铋反應造成的二維態被觀察到。除此之外，我們使用光電子能譜去調查錫烯跟碲化铋之間的鍵結情形。我們提出可能的鍵結情況跟為何在角解析電子能譜中K 點上觀察不到狄拉克錐。
高品質的阿法錫薄膜可以藉由分子束磊晶長在銻化銦基板上。繞射圖指出只有阿法 態的錫長在銻化銦基板上。清楚的塊材能帶跟兩個拓樸表面態可以在我們三十層的阿法錫/銻化銦的角解析電子能譜中觀察到。阿法錫的費米能階可以藉由改變成長速度來調變。低鍍率樣品的費米能階坐落在上狄拉克錐，而且看不到導帶，這代表阿法錫的能隙比0.1eV來的大。這些結果指出阿法錫是一個理想的拓樸絕緣體，傳輸性質主要由表面態貢獻。

Topological insulators (TI), a new state of quantum matter, have received unparalleled attentions in recent years in the scientific community due to exotic physical properties such as a time reversal symmetry protected surface state and potential applications in dissipationless electronics and quantum computing.

In this dissertation, the study was focused on properties of topological insulators grown by molecular beam epitaxy. High quality Bi2Se3 thin films were obtained via van der Waals epitaxy in various substrates. Sharp surface state and Dirac cone were observed in our ARPES spectra of Bi2Se3 on various substrates. However, the Fermi level of Bi2Se3 is always located in bulk conduction band due to intrinsic defects. This indicates the bulk bands also contribute to the transport.

Besides, we report a crystalline Se capping layer obtained by a new growth method. Upon extended exposure to UHV or humid air, we show by x-ray photoemission spectroscopy (XPS) that the stability and resistance to oxidation of crystalline Se capping layers are superior to that of amorphous Se capping layer, which has been commonly used by current communities. Furthermore, time-dependent Hall measurements showed crystalline Se capping layers had a much stronger ability to sustain the intrinsic transport properties of Bi2Se3.

In order to let the transport dominated by the surface state, we look for an elemental material which is also a TI. Thin film Sn provides several advantages: With its elemental nature, Sn is free from the stoichiometry issue and the related defect problems in compound TI families. It also offers potentially rich structures with different band diagram spanning from 3-D TI to 2-D TI. We have successfully grown monolayer Sn film with stanene like structure on the Bi2Te3 substrate. The electronic structures of epitaxial stanene films were determined by ARPES. The hole bands of stanene were observed at the Garmma point with additional 2D states which come from the reaction between stanene and Bi2Te3. Furthermore, we investigate the bonding configuration during the growth of Stanene by XPS and pointed out a possible bonding configuration and the reason why the Dirac like the state is not observed at the K point in the ARPES spectrum.

High quality Alpha-Sn films were attained on InSb(001) by MBE. The XRD scans show only Alpha phase Sn was grown on InSb(001) with clear Pendellösung fringes. Clear bulk bands (Γ_8^+, Γ_7^+, Γ_7^-) and two TSSs were observed in our ARPES spectrum of 30BL Alpha-Sn on InSb(001). Besides, the Fermi level of Alpha-Sn can be tuned by varying the growth rate of Alpha-Sn. The Fermi level of low growth rate sample is located in the top of Dirac cone without overlapping with bulk conduction band. This indicates the band gap is larger than 0.1eV. These results suggest Alpha-Sn is an ideal topological insulator, whose transport properties dominated by the topological surface state.

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