臺灣博碩士論文加值系統

我們以自我助熔法成長四鉛化鉑(PtPb4)單晶，在經由X光繞射量測確認PtPb4晶體後，進行了電性及磁性量測，可發現其Tc約為2.77 K。由磁場下電阻-溫度的行為，我們獲得了上臨界磁場Hc2、相干長度 ξ 與溫度之關係及釘扎能U和磁場之關係；由磁化強度M-H之關係，我們獲得下臨界磁場Hc1、穿透深度λ、與溫度，及釘扎能與外加磁場之關係。此外，由霍爾電性量測亦發現PtPb4主要傳輸載子在31 K以下為電子，31 K以上則轉變為電洞。在正常態，我們發現PtPb4的磁阻(magnetoresistance, MR)在高磁場下和外加磁場呈線性關係，在磁場6 T溫度5 K下，其磁阻可達300%，而推測其線性磁阻之現象可利用Parish and Littlewood model(PL model)來解釋，其低溫5 K之磁阻亦顯示PtPb4具有拓樸表面態之弱反局域(weak-anti-localization)電導特性。由M-H量測可顯示PtPb4之二類超導磁場穿透性質。透過磁滯曲線，我們可以利用Bean model得到臨界電流密度，進而得到釘扎力隨磁場之變化關係，最後利用Dew-Hughes model來擬合結果，發現PtPb4在低溫2.0 K為一維磁通釘扎，溫度往Tc升高時開始偏向二維磁通釘扎。

PtPb4 single crystals have been grown with self-flux method. After we determine the crystals of PtPb4 with X-ray diffraction, we measure its electric as well as magnetic properties, realizing that the critical temperature Tc is about 2.77 K. According to the characteristic of resistance-temperature behavior under magnetic fields applied, we have obtained the temperature dependances of the upper critical field Hc2(T), coherence length ξ(T), as well as field dependance of pinning energy U(H). From the diagram of field-dependent magnetization M(H) curves, we have obtained the temperature dependances of lower critical field Hc1(T), and penetration depth λ(T). Besides, from the results of Hall measurement, we have noticed that the main carriers below 31 K are electrons, but they transform into holes at temperatures higher than 31 K. At normal state, it is worth noticed that the magnetoresistance (MR) of PtPb4 exhibits a linear correlation with the applied magnetic field at high fields, and reaches to 300 % under 6 T and 5 K. It is predicted that this phenomenon can be described by the Parish and Littlewood (PL) model. The MR behavior of PtPb4 at 5 K indicate that there is a topological surface state existing on PtPb4, accompanying a weak-anti-localization (WAL) conductivity observed. Results of M-H measurements clearly reveal the type-II superconductivity in PtPb4. From magnetic hysteresis loop, we have obtained the critical current density Jc base on the Bean model, and further derived the variation of pinning force Fp at different applied fields. Finally, we use the Dew-Hughes model to fit the result Fp(H) data, and find that PtPb4 exhibits one-dimensional flux-pinning at lower temperature of 2.0 K, then the flux pinning transforms to be two-dimensional as the temperature gets higher and near Tc.

致謝 ii
摘要 iv
Abstract v
目錄 vi
圖目錄 ix
表目錄 xii
第一章 緒論 1
1-1 研究背景 1
1-1-1 超導體簡介 1
1-1-2 拓撲學及拓樸材料 2
1-1-3 四鉛化鉑(PtPb4)及其文獻探討 3
1-2 研究動機 4
第二章 理論背景與原理簡介 5
2-1 超導體特性 5
2-1-1 零電阻 5
2-1-2 反磁性(diamagnetism) 6
2-1-3 倫敦穿透深度(London penetration depth) 7
2-1-4 二流體模型(Two-fluid model) 8
2-1-5 臨界電流(critical current)及臨界磁場(critical magnetic field) 9
2-1-6 Anderson-Kim 磁通蠕動模型 15
2-1-7 相干長度(coherence length) 17
2-2 霍爾效應(Hall effect) 18
2-3 磁阻(Magnetic resistance, MR) 19
2-3-1 定義 19
2-3-2 Parish and Littlewood model (PL model) 20
2-3-3 弱局域效應(weak localization, WL)及弱反局域效應(weak anti-localization, WAL) 22
第三章 實驗方法 23
3-1 實驗流程 23
3-2 四鉛化鉑(PtPb4)樣品合成 24
3-3 量測系統 26
3-3-1 X光繞射分析儀(X-ray Diffractometer, XRD) 26
3-3-2 SQUID量測系統 27
第四章 實驗結果與數據討論 29
4-1 樣品結構 29
4-1-1 XRD量測 29
4-2 基本超導特性 30
4-2-1 電阻率(ρ)對溫度(T)關係 30
4-2-2 磁化率(M)對溫度(T)關係 31
4-3 電性量測結果 32
4-3-1 臨界溫度(Tc)附近縱向電阻率(ρ_xx)與溫度(T)關係 32
4-3-2 上臨界磁場(Hc2) 33
4-3-3 0-300 K之縱向電阻率(ρ_xx)與溫度(T)關係 34
4-3-4 由ρ_xx-T分析釘扎能(pinning energy) 34
4-3-5 縱向電阻率(ρ_xx)與外加磁場(H)關係 37
4-3-6霍爾係數(Hall coefficient, RH)及橫向電阻率(ρ_xy)與溫度(T)關係 38
4-3-7 載子濃度(carrier concentration, n)及霍爾遷移率(Hall mobility, μ)與溫度(T)關係 40
4-3-8 橫向電阻率(ρ_xx)與外加磁場(H)關係 41
4-4 磁性量測結果 43
4-4-1 磁化強度(M)對外加磁場(H)關係 43
4-4-2 臨界磁場(Hc1 & Hc2)對溫度(T)關係 45
4-4-3 相干長度(coherence length, ξ)與倫敦穿隧深度(London penetration depth, λ) 48
4-4-4 磁滯曲線(magnetic hysteresis loop) 50
4-4-5 臨界電流密度(critical current density)與釘扎力(pinning force) 52
4-5 磁阻分析 54
4-5-1 磁阻(MR)對溫度(T)及外加磁場(H)之關係 54
4-5-2 磁阻(MR)對霍爾遷移率(μ)及載子濃度(n) 55
4-5-3 弱反局域效應(WAL)分析 57
第五章 結論 59
參考文獻 60

[1] H. K. Onnes. Leiden Comm., vol. 122b, p. 122c, (1911).
[2] W. Meissner, R. Ochsenfeld. Naturwiss, vol. 787, p. 21, (1933).
[3] J. Bardeen, L.N. Copper, J. R. Schrieffer. Phys. Rev., vol. 108, (1957).
[4] J. G. Bednorz et al. Z Phys. B, vol. 64, p.189, (1986).
[5] P. J. Ray. “Structural investigation of La(2-x)SrxCuO(4+y)-Following staging as a fumction of temperature”. master thesis of University of Copenhagen, (2015).
[6] X. Kou, Y. Fan, M. Lang, P. Upadhyaya, K. L. Wang. Solid State Communications, 215-216, p. 34, (2015).
[7] D. Shen, C. N. Kuo, T. W. Yang, I. N. Chen, C. S. Lue, L. M. Wang. Commun. Mater. 1, 56, (2020).
[8] U. Rosler and K. Schuber. Naturwiss, 38, 331, (1951).
[9] M.F Gendron, R.E Jones. J. Phys. Chem. Solids, vol., p. 405, (1962).
[10] B. T. Matthias. Progress in Low-Temperature Physics. vol., 2, (1957).
[11] Alekseev, E. S. Popova, S. V. Larchev. J. Alloys Comp., vol. 176, 1–6, (1991).
[12] C. P. Poole and H. A. Farach, J. Supercond., 13, 47, (2000).
[13] Z. H. Long, X. M. Tao, H. S. Liu, and Z. P. Jin. J. Phase Equilib. Diffus., vol. 30, p.318, (2009).
[14] 沈棟。「四錫化鉑、四錫化金和四鉛化鉑單晶之電磁傳輸特性的研究」。國立臺灣大學物理學研究所博士論文，(2020)。
[15] K. Lee et al. “Evidence for large Rashba splitting in PtPb4 from Angle-Resolved Photoemission Spectroscopy”, unpublished.
[16] D. J. Quinn. J. Appl. Phys., vol. 33, p. 748, (1962).
[17] F. London and H. London. Proc. Roy Soc., A155, (1935)
[18] 張裕恆、李玉芝。超導物理， (2009)。
[19] C. P. Bean. Phys. Rev. Lett., vol. 8, p.250, (1962).
[20] P. W. Anderson, and Y. B. Kim. Rev. of Mod. Phys., vol. 36, p. 39, (1964).
[21] C. Kittel. Introduction to Solid state Physics, (8th ed.), (2005).
[22] S. M. Grivin, K. Yang. Modern Condensed Physics, (2019).
[23] E. Hall, Am. J. Math, 2, p.287, (1879).
[24] D. A. Neamen. Microelectronics: Circuit Analysis and Design, (5th ed.), (2010).
[25] B. D. Cullity. Introduction to Magnetic Materials, (1972).
[26] R. Xu, A. Husmann, T. F. Rosenbaum, M.-L. Saboungi, J. E. Enderbya, and P. B. Littlewood. Nature, 390, 57, (1997).
[27] M. M. Parish and P. B. Littlewood. Nature, 426, 162–165, (2003).
[28] S. Hikami, A. I. Larkin, and Y. Nagaoka. Progress of Theoretical Physics, vol. 63(2), p. 707-710, (1980).
[29] R. Lbibb et al. J. Alloys Compd., 302, 155, (2000).
[30] W. H. Bragg and W. L. Bragg. Proc. R. Soc. Lond. A, 88, (1913).
[31] [online]. Available: http://materialsproject.org
[32] P.H. Yin, R.F. Xiao, X.C. Xu, T.F. Duan, Z.H. Wang. Physica C, 542, (2017).
[33] 馬沛綸。「高溫超導釔鋇銅氧薄膜之反鄰近效應研究與碲化鉍/釔鋇銅氧之拓樸/超導異質界面特性之研究」。國立臺灣大學物理學研究所碩士論文，(2018)。
[34] 王碩宏。「鐵插碲化鉍單晶之電磁傳輸特性研究」。國立臺灣大學理學院物理學研究所碩士論文，(2019)。
[35] S. Sun et al. News J. Phys. vol. 18, 082002, (2016).
[36] R. D. Parks. Superconductivity, vol. 2, (1969).
[37] G. J. C. Bots et al. Physica, 31, 1113, (1965).
[38] D. Dew-Hughes. Philosophical Magazine, vol. 30:2, pp. 293-305, (1974).
[39] U.C. Sou et al. Chinese Journal of Physics, 43, (2005).