為了嘗試以人工創造的方式，探尋合成拓樸超導體之可能，本研究嘗試尋找合適的材料以實現此目的。理論預測曾提出許多種形式可實現這樣的可能性，而其中一種形式即透過將磁性奈米島嶼擺放在s-wave超導體材料上，以找尋自旋手性之馬約拉納邊界態。本實驗研究最主要透過將常見之鐵磁性原子Ni鍍在Pb(111)基板上，以形成鎳鉛表面合金以及單層之鎳奈米島嶼，使其成為二維磁性奈米島嶼生長於s-wave超導體材料之系統，並以自旋極化之掃描穿隧顯微鏡（Spin-polarized scanning tunneling microscopy）以及掃描穿隧能譜技術（Scanning tunneling spectroscopy），搭配理論計算解析二維磁性材料於超導體之上之原子結構和電子結構。改變鍍膜時之成長溫度與後退火溫度，會導致不同之成長模式與結構，根據由原子尺度下地形地貌所推導之結構模型，雙層的鎳鉛合金第一層由Ni2Pb1的比例組成穩定之六方晶格結構，二層結構則為鎳原子嵌入排列至頂層鉛吸附原子下之結果，並形成四方與六方晶格結構。基於掃描穿隧能譜的量測，鎳鉛合金之超導能隙（Superconducting gap）為ΔNiPb ≈ 0.85 meV，對比鉛的超導能隙為ΔPb ≈ 0.97 meV要來得小；而單層鎳鉛奈米島上會形成蜂巢結構，其超導能隙為ΔNi ≈ 0.97 meV大小與鉛基板相同。其二者與鉛塊材基板的超導曲線，藉由將樣品溫度逐漸升高，皆至同樣的臨界溫度6.70 K後消失。其鎳鉛合金與單層鎳奈米島之超導能隙要小於等於鉛，並且兩者皆為在同樣的臨界溫度喪失超導態，此二者皆可提供其可能為透過鄰近效應所引發超導態之證據。此外，藉由量測鎳鉛合金與Pb(111)間由鄰近效應所影響而逐漸遞減之邊界，其超導衰退長度（Decay length）ξL約為4 nm，鎳鉛合金其超導能隙之遞減，最主要的原因可能由於受到其磁性來源之抑制，這也表示其磁性可與超導同時共存，使得磁性材料和超導體材料結合以實現拓樸超導體提供了可能性。

In order to fabricate topological superconductors artificially, we attempt to find suitable material to realize this purpose. One of the models has been proposed to find the chiral Majorana edge states, and it can be created by placing magnetic nanoislands on the surface of s-wave superconductors. In this study, we have investigated proximity-induced superconductivity in monatomic Ni-Pb alloy and Ni nanoisland grown on Pb(111) by STM and STS measurement with theoretical calculations. The growth of different structural phases will highly depend on evaporating and post-annealing temperatures. The topography images and first-principle calculations of bilayer Ni-Pb alloy shows it will form a rectangular and hexagonal lattice. Differential conductance spectra have resolved induced superconductivity on Ni-Pb alloy with gap size ΔNiPb ≈ 0.85 meV, which is smaller than the gap value delta ΔPb ≈ 0.97 meV on Pb(111). Also, Ni nanoislands with honeycomb lattice display an induced superconductivity gap size the same with Pb(111) substrate. Among them, increasing temperature leads to the absence of the superconducting gap, all critical temperatures are 6.70 K and are consistent with the BCS fitting. These results support the superconductivity on the Ni-Pb alloy and Ni nanoislands, which are induced by the proximity effect. Furthermore, with the spatial variation of the superconducting gap across from Ni-Pb alloy and substrate, extract the value beside the boundary shows the decay length is about 4 nm. Such a rather short decay length and a reduced superconductivity gap indicate a magnetic contribution, which turns superconducting Ni-Pb surface alloy into a potential template for realizing a 2D magnetic-superconductor hybrid system.

摘要 - I
Abstract - III
致謝 - V
目錄 - VI
圖目錄 - VIII
表目錄 - XIII
第一章 簡介（Introduction） - 1
1.1. 研究動機（Motivation） - 1
1.1.1. 概觀 - 1
1.1.2. 鉛基板之相關系統文獻 - 2
1.1.3. 超導之相關系統文獻 - 5
1.2. 超導（Superconductivity） - 6
1.3. 馬約拉納費米子（Majorana fermions） - 8
1.4. 拓樸超導體（Topological superconductor） - 9
1.4.1. 拓樸之概念 - 9
1.4.2. 拓樸絕緣體之簡介 - 10
1.4.3. 拓樸超導體之簡介 - 12
第二章 實驗儀器與工作原理（Experimental apparatus） - 16
2.1. 超高真空系統（Ultra-high vacuum systems） - 16
2.1.1. 真空的定義與分類 - 17
2.1.2. 真空抽氣系統 - 17
2.1.3. 真空氣壓計 - 20
2.1.4. 殘餘氣體分析儀 - 22
2.2. 薄膜成長（Thin film growth） - 25
2.2.1. 分子束磊晶法 - 25
2.2.2. 薄膜成長模式 - 27
2.3. 自旋極化掃描穿隧顯微鏡（Spin-polarized scanning tunneling microscopy；SP-STM） - 28
2.3.1. 量子穿隧效應 - 29
2.3.2. Tersoff—Hamann微擾近似理論 - 30
2.3.3. 掃描穿隧能譜 - 33
2.3.4. 自旋極化之穿隧效應 - 34
2.3.5. 儀器構造 - 37
2.3.6. 取像模式 - 40
第三章 實驗結果與討論（Results and discussion） - 42
3.1. 樣品製備（Sample preparation） - 43
3.1.1. 鎳鉛表面合金之製備流程 - 43
3.1.2. 鎳鉛表面合金薄膜之成長與討論 - 44
3.1.3. 單層鎳奈米島嶼之製備流程 - 47
3.1.4. 單層鎳奈米島嶼之成長與討論 - 48
3.2. 鎳鉛之表面合金（Nickel-Lead surface alloy） - 51
3.3. 單層鎳奈米島嶼（Nickel nanoislands） - 59
第四章 結論（Conclusion） - 65
參考文獻 - 67

[1] A. Y. Kitaev, Ann. Phys. 303, 2 (2003).
[2] C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma, Rev. Mod. Phys. 80, 1083 (2008).
[3] L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008).
[4] P. de Gennes, Rev. Mod. Phys. 36, 225 (1964).
[5] J. Hauser, H. Theuerer, and N. Werthamer, Phys. Rev. 142, 118 (1966).
[6] C. W. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
[7] C. Lambert and R. Raimondi, J. Phys. Condens. Matter 10, 901 (1998).
[8] V. Mourik, K. Zuo, S. M. Frolov, S. Plissard, E. P. Bakkers, and L. P. Kouwenhoven, Science 336, 1003 (2012).
[9] S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. Marcus, Nature 531, 206 (2016).
[10] S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Science 346, 602 (2014).
[11] M. Ruby, B. W. Heinrich, Y. Peng, F. von Oppen, and K. J. Franke, Nano Lett. 17, 4473 (2017).
[12] A. Palacio-Morales, E. Mascot, S. Cocklin, H. Kim, S. Rachel, D. K. Morr, and R. Wiesendanger, Sci. Adv. 5, eaav6600 (2019).
[13] G. C. Ménard, A. Mesaros, C. Brun, F. Debontridder, D. Roditchev, P. Simon, and T. Cren, Nat. Commun. 10, 1 (2019).
[14] M. Müller, N. Néel, S. Crampin, and J. Kröger, Phys. Rev. Lett. 117, 136803 (2016).
[15] M. Müller, N. Néel, S. Crampin, and J. Kröger, Phys. Rev. B 96, 205426 (2017).
[16] S. Y. Song and J. Seo, Sci. Rep 7, 1 (2017).
[17] T. Zhang et al., Nat. Phys. 6, 104 (2010).
[18] C. Brun et al., Nat. Phys. 10, 444 (2014).
[19] S. Qin, J. Kim, Q. Niu, and C.-K. Shih, Science 324, 1314 (2009).
[20] S.-H. Ji, T. Zhang, Y.-S. Fu, X. Chen, X.-C. Ma, J. Li, W.-H. Duan, J.-F. Jia, and Q.-K. Xue, Phys. Rev. Lett. 100, 226801 (2008).
[21] Y. Kamihara, H. Hiramatsu, M. Hirano, R. Kawamura, H. Yanagi, T. Kamiya, and H. Hosono, J. Am. Chem. Soc. 128, 10012 (2006).
[22] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).
[23] F.-C. Hsu et al., PNAS 105, 14262 (2008).
[24] W. Qing-Yan et al., Chinese Physics Letters 29, 037402 (2012).
[25] S. He et al., Nat. Mater. 12, 605 (2013).
[26] J.-F. Ge, Z.-L. Liu, C. Liu, C.-L. Gao, D. Qian, Q.-K. Xue, Y. Liu, and J.-F. Jia, Nat. Mater. 14, 285 (2015).
[27] S. Manna et al., Nat. Commun. 8, 1 (2017).
[28] L. N. Cooper, Phys. Rev. 104, 1189 (1956).
[29] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
[30] A. P. Mackenzie and Y. Maeno, Rev. Mod. Phys. 75, 657 (2003).
[31] C. Tsuei and J. Kirtley, Rev. Mod. Phys. 72, 969 (2000).
[32] P. A. M. Dirac, Proc. R. Soc. A 117, 610 (1928).
[33] P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[34] C. D. Anderson, Phys. Rev. 43, 491 (1933).
[35] E. Majorana, Nuovo Cimento 14, 171 (1937).
[36] M. Sato and Y. Ando, Rep. Prog. Phys. 80, 076501 (2017).
[37] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
[38] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
[39] M. Kohmoto, Ann. Phys. 160, 343 (1985).
[40] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005).
[41] N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).
[42] A. Y. Kitaev, Phys.-Uspekhi 44, 131 (2001).
[43] C. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013).
[44] M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. Lett. 103, 020401 (2009).
[45] J. Linder, Y. Tanaka, T. Yokoyama, A. Sudbø, and N. Nagaosa, Phys. Rev. Lett. 104, 067001 (2010).
[46] I. Bello, Vacuum and Ultravacuum: Physics and Technology (CRC Press, 2017).
[47] 伍秀菁、汪若文、林美吟編輯, 真空技術與應用 (國科會精密儀器發展中心, 民90).
[48] SRS, Models RGA100, RGA200, and RGA300 Residual Gas Analyzer (Stanford Research Systems, Inc., 2009).
[49] W. Paul, Rev. Mod. Phys. 62, 531 (1990).
[50] FOCUS, Instruction Manual UHV Evaporator EFM 2/3(s)/4(s) Triple Evaporator EFM 3T(s) IBAD Evaporator EFM 3i (FOCUS GmbH., 2017).
[51] G. Binning and H. Rohrer, Helv. Phys. Acta 55, 276 (1982).
[52] C. J. Chen, Introduction to Scanning Tunneling Microscopy (Oxford University Press, 2008), 2nd edn.
[53] R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009).
[54] J. Bardeen, Phys. Rev. Lett. 6, 57 (1961).
[55] J. Tersoff and D. R. Hamann, Phys. Rev. B 31, 805 (1985).
[56] J. Tersoff and D. R. Hamann, Phys. Rev. Lett. 50, 1998 (1983).
[57] I. Giaever, Phys. Rev. Lett. 5, 147 (1960).
[58] I. Giaever, Phys. Rev. Lett. 5, 464 (1960).
[59] I. Giaever and K. Megerle, Phys. Rev. 122, 1101 (1961).
[60] M. Julliere, Phys. Lett. A 54, 225 (1975).
[61] J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. Lett. 74, 3273 (1995).
[62] W. Butler, X.-G. Zhang, T. Schulthess, and J. MacLaren, Phys. Rev. B 63, 054416 (2001).
[63] S. S. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant, and S.-H. Yang, Nature materials 3, 862 (2004).
[64] S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, and K. Ando, Nat. Mater. 3, 868 (2004).
[65] Y. V. Fominov, N. Chtchelkatchev, and A. Golubov, Phys. Rev. B 66, 014507 (2002).