本論文透過電阻率與比熱量測，探討 NiBi3 單晶在低溫下的超導性質。儘管先前研究認為 NiBi3 是全能隙、單能隙的 ?-wave 超導體，我們的實驗結果顯示其超導行為更加複雜。電子比熱係數 ?(?) 隨磁場變化呈現明顯彎折現象，而超導臨界溫度?c以下的比熱溫度依賴性則更適合以雙能隙 ?-wave 模型描述，而非單能隙或線性節點模型。此外，上臨界磁場 ?c2 (?) 的變化趨勢符合 Ginzburg–Landau 方程的預測，並符合傳統 BCS 理論架構。我們在比熱與電阻率數據中皆未觀察到內在鐵磁性的證據。
本研究結果確認 NiBi3 為一種具備雙能隙 ?-wave 結構的傳統超導體，且不具內在磁序，為其能隙結構提供了嶄新的理解。

In this thesis, we investigate the superconducting properties of NiBi3 single crystals through resistivity and specific heat measurements down to low temperatures. While earlier studies suggested that NiBi3 exhibits fully gapped, single-gap ?-wave superconductivity, our experimental results reveal a more complex superconducting behavior. The magnetic field dependence of the electronic specific heat coefficient ?(?) displays a clear kink, and the temperature dependence of the specific heat below ?c is best described by a two-gap ?-wave model rather than single-gap or line-node models. In addition, the upper critical field ?c2 (?) behavior is consistent with predictions from the Ginzburg–Landau equation and can be understood within the framework of conventional BCS theory. No evidence of intrinsic ferromagnetism was found in either the specific heat or resistivity data.
Our findings establish that NiBi3 is a two-gap ?-wave conventional superconductor without intrinsic magnetic ordering, providing new insight into its gap structure.

[1] H. Kamerlingh-Onnes. The resistance of pure mercury at helium temperatures. Communications from the Physical Laboratory of the University of Leiden, 122:13–15, 1911.
[2] Vladimir Kozhevnikov. Meissner effect: History of development and novel aspects. Journal of Superconductivity and Novel Magnetism, 34(8):1979–2009, Aug 2021.
[3] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 2 - the phenomenon of superconductivity. In Charles P. Poole, Horacio A. Farach, and Richard J. Creswick, editors, Superconductivity, pages 21–58. Academic Press, 1995.
[4] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 5 - ginzburg–landau theory. In Charles P. Poole, Horacio A. Farach, and Richard J. Creswick, editors, Superconductivity, pages 121–148. Academic Press, 1995.
[5] C. Kittel. Introduction to solid state physics. NY: John Wiley & Sons, 2004.
[6] F. Bouquet, Y. Wang, R. A. Fisher, D. G. Hinks, J. D. Jorgensen, A. Junod, and N. E. Phillips. Phenomenological two-gap model for the specific heat of mgb2. Europhysics Letters, 56(6):856, dec 2001.
[7] P. Szabó, P. Samuely, J. Kačmarčík, T. Klein, J. Marcus, D. Fruchart, S. Miraglia, C. Marcenat, and A. G. M. Jansen. Evidence for two superconducting energy gaps in mgb2 by point-contact spectroscopy. Phys. Rev. Lett., 87:137005, Sep 2001.
[8] James William Quilty. The mgb2 superconducting energy gaps measured by raman spectroscopy. Physica C: Superconductivity, 385(1):264–272, 2003.
[9] Guglielmo Ventura and Lara Risegari. The Art of Cryogenics. Elsevier Science, 2008.
[10] G. Teleberg G. Batey. Principles of dilution refrigeration. 2015.
[11] R. Bachmann, Jr. DiSalvo, F. J., T. H. Geballe, R. L. Greene, R. E. Howard, C. N. King, H. C. Kirsch, K. N. Lee, R. E. Schwall, H.-U. Thomas, and R. B. Zubeck. Heat capacity measurements on small samples at low temperatures. Review of Scientific Instruments, 43(2):205–214, 02 1972.
[12] J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Theory of superconductivity. Phys. Rev., 108:1175–1204, Dec 1957.
[13] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 4 - thermodynamic properties. In Charles P. Poole, Horacio A. Farach, and Richard J. Creswick, editors, Superconductivity, pages 91–119. Academic Press, 1995.
[14] Norman E. Phillips. Low-temperature heat capacities of gallium, cadmium, and copper. Phys. Rev., 134:A385–A391, Apr 1964.
[15] Norman E. Phillips. Heat capacity of aluminum between 0.1°k and 4.0°k. Phys. Rev., 114:676–685, May 1959.
[16] Xinxin Gong, Mehdi Kargarian, Alex Stern, Di Yue, Hexin Zhou, Xiaofeng Jin, Victor M. Galitski, Victor M. Yakovenko, and Jing Xia. Time-reversal symmetry-breaking superconductivity in epitaxial bismuth/nickel bilayers. Science Advances, 3(3):e1602579, 2017.
[17] Junhua Wang, Xinxin Gong, Guang Yang, Zhaozheng Lyu, Yuan Pang, Guangtong Liu, Zhongqing Ji, Jie Fan, Xiunian Jing, Changli Yang, Fanming Qu, Xiaofeng Jin, and Li Lu. Anomalous magnetic moments as evidence of chiral superconductivity in a bi/ni bilayer. Phys. Rev. B, 96:054519, Aug 2017.
[18] P. LeClair, J. S. Moodera, J. Philip, and D. Heiman. Coexistence of ferromagnetism and superconductivity in Ni/Bi bilayers. Phys. Rev. Lett., 94:037006, Jan 2005.
[19] Matthew Vaughan, Nathan Satchell, Mannan Ali, Christian J. Kinane, Gavin B. G. Stenning, Sean Langridge, and Gavin Burnell. Origin of superconductivity at nickel-bismuth interfaces. Phys. Rev. Res., 2:013270, Mar 2020.
[20] L. Y. Liu, Y. T. Xing, I. L. C. Merino, H. Micklitz, D. F. Franceschini, E. Baggio-Saitovitch, D. C. Bell, and I. G. Solórzano. Superconductivity in bi/ni bilayer system: Clear role of superconducting phases found at bi/ni interface. Phys. Rev. Mater., 2:014601, Jan 2018.
[21] Esmeralda Lizet Martinez Piñeiro, Brenda Lizette Ruiz Herrera, Roberto Escudero, and Lauro Bucio. Possible coexistence of superconductivity and magnetism in intermetallic nibi3. Solid State Communications, 151(6):425–429, 2011.
[22] B. Silva, R. F. Luccas, N. M. Nemes, J. Hanko, M. R. Osorio, P. Kulkarni, F. Mompean, M. García-Hernández, M. A. Ramos, S. Vieira, and H. Suderow. Superconductivity and magnetism on flux-grown single crystals of nibi3. Phys. Rev. B, 88:184508, Nov 2013.
[23] T. Herrmannsdörfer, R. Skrotzki, J. Wosnitza, D. Köhler, R. Boldt, and M. Ruck. Structure-induced coexistence of ferromagnetic and superconducting states of single-phase bi3ni seen via magnetization and resistance measurements. Phys. Rev. B, 83:140501, Apr 2011.
[24] T. Shang, J. Meng, X. Y. Zhu, H. Zhang, B. C. Yu, Z. X. Zhen, Y. H. Wang, Y. Xu, Q. F. Zhan, D. J. Gawryluk, and T. Shiroka. Fully gapped superconductivity with preserved time-reversal symmetry in nibi3 single crystals. Phys. Rev. B, 107:174513, May 2023.
[25] Yasunobu Fujimori, Shin-ichi Kan, Bunjyu Shinozaki, and Takasi Kawaguti. Superconducting and normal state properties of nibi 3. Journal of the Physical Society of Japan, 69(9):3017–3026, 2000.
[26] Jagdish Kumar, Anuj Kumar, Arpita Vajpayee, Bhasker Gahtori, Devina Sharma, P K Ahluwalia, S Auluck, and V P S Awana. Physical property and electronic structure characterization of bulk superconducting bi3ni. Superconductor Science and Technology, 24(8):085002, jun 2011.
[27] Jingyuan Wang, Camron Farhang, Di Yue, Xiaofeng Jin, Xiangde Zhu, and Jing Xia. Absence of spontaneous time-reversal symmetry breaking and ferromagnetism in superconducting Nibi3 single crystal. Phys. Rev. B, 107:024415, Jan 2023.
[28] Xiangde Zhu, Hechang Lei, Cedomir Petrovic, and Yuheng Zhang. Surface-induced magnetic fluctuations in a single-crystal nibi3 superconductor. Phys. Rev. B, 86:024527, Jul 2012.
[29] Gladys H. Fuller. Nuclear spins and moments. Journal of Physical and Chemical Reference Data, 5(4):835–1092, 10 1976.
[30] P.-Y. Cheng, Mohamed Oudah, T.-L. Hung, C.-E. Hsu, C.-C. Chang, J.-Y. Haung, T.-C. Liu, C.-M. Cheng, M.-N. Ou, W.-T. Chen, L. Z. Deng, C.-C. Lee, Y.-Y. Chen, C.-N. Kuo, C.-S. Lue, Janna Machts, Kenji M. Kojima, Alannah M. Hallas, and C.-L. Huang. Physical properties and electronic structure of the two-gap superconductor v2ga5. Phys. Rev. Res., 6:033253, Sep 2024.
[31] L. Shan, Z. Y. Liu, Z. A. Ren, G. C. Che, and H. H. Wen. Competition between bcs superconductivity and ferromagnetic spin fluctuations in MgCni3. Phys. Rev. B, 71:144516, Apr 2005.
[32] T. Klimczuk, F. Ronning, V. Sidorov, R. J. Cava, and J. D. Thompson. Physical properties of the noncentrosymmetric superconductor mg10ir19b16. Phys. Rev. Lett., 99:257004, Dec 2007.
[33] J. S. Kim, R. K. Kremer, L. Boeri, and F. S. Razavi. Specific heat of the ca-intercalated graphite superconductor cac6. Phys. Rev. Lett., 96:217002, Jun 2006.
[34] J. Chen, L. Jiao, J. L. Zhang, Y. Chen, L. Yang, M. Nicklas, F. Steglich, and H. Q. Yuan. Bcs-like superconductivity in the noncentrosymmetric compounds nbx re1−x (0.13 ≤ x ≤ 0.38). Phys. Rev. B, 88:144510, Oct 2013.
[35] Y. Xu, S. Jöhr, L. Das, J. Kitagawa, M. Medarde, T. Shiroka, J. Chang, and T. Shang. Crossover from multiple- to single-gap superconductivity in nb5ir3−x ptx O alloys. Phys. Rev. B, 101:134513, Apr 2020.
[36] M. Nohara, H. Suzuki, N. Mangkorntong, and H. Takagi. Impurity-induced gap renormalization in anisotropic superconductors: Mixed-state specific heat of la2xsrx(cu1yzny)o4 and y(ni1xptx)2b2c. Physica C: Superconductivity, 341-348:2177–2180, 2000. Proceedings of the International Conference on Materials and Mechanisms of Superconductivity High Temperature Superconductors VI.
[37] H.D. Yang and J.-Y. Lin. Low temperature specific heat studies on the pairing states of high-tc superconductors: a brief review. Journal of Physics and Chemistry of Solids, 62(9):1861–1870, 2001.
[38] N. E. Phillips, B. Buffeteau, R. Calemczuk, K. W. Dennis, J. P. Emerson, R. A. Fisher, J. E. Gordon, T. E. Hargreaves, C. Marcenat, R. W. McCallum, A. S. O'Connor, A. Schilling, B. F. Woodfield, and D. A. Wright. Specific heat of yba2cu3o7 δ and (la2xsrx)cuo4: Evidence for d-wave pairing. Journal of Superconductivity, 12(1):105–111, Feb 1999.
[39] Shusaku Imajo, Naoki Kanda, Satoshi Yamashita, Hiroki Akutsu, Yasuhiro Nakazawa, Hiroya Kumagai, Takuya Kobayashi, and Atsushi Kawamoto. Thermodynamic evidence of d-wave superconductivity of the organic superconductor λ-(bets)2gacl4. Journal of the Physical Society of Japan, 85(4):043705, 2016.
[40] Minoru Nohara, Masanobu Isshiki, Hidenori Takagi, and Robert J. Cava. Magnetic field dependence of the low-temperature specific heat of the borocarbide superconductor luni2b 2c. Journal of the Physical Society of Japan, 66(7):1888–1891, 1997.
[41] C. L. Huang, J.-Y. Lin, Y. T. Chang, C. P. Sun, H. Y. Shen, C. C. Chou, H. Berger, T. K. Lee, and H. D. Yang. Experimental evidence for a two-gap structure of superconducting Nbse2: A specific-heat study in external magnetic fields. Phys. Rev. B, 76:212504, Dec 2007.
[42] Costel R. Rotundu, Thomas R. Forrest, Norman E. Phillips, and Robert J. Birgeneau. Specific heat of ba0.59k0.41fe2as2, an fe-pnictide superconductor with tc = 36.9 k, and a new method for identifying the electron contribution. Journal of the Physical Society of Japan, 84(11):114701, 2015.
[43] Yue Sun, Yi Ding, Dongmei Gu, Jinchen Zhuang, Zhixiang Shi, and Tsuyoshi Tamegai. Specific heat and upper critical field of sc5ir4si10 superconductor. Journal of the Physical Society of Japan, 82(7):074713, 2013.
[44] F. Bouquet, R. A. Fisher, N. E. Phillips, D. G. Hinks, and J. D. Jorgensen. Specific heat of mg11 B2: Evidence for a second energy gap. Phys. Rev. Lett., 87:047001, Jul 2001.
[45] J T Chen, Y Sun, T Yamada, S Pyon, and T Tamegai. Two-gap features revealed by specific heat measurements in fese. Journal of Physics: Conference Series, 871(1):012016, jul 2017.
[46] T Shang, W Xie, D J Gawryluk, R Khasanov, J Z Zhao, M Medarde, M Shi, H Q Yuan, E Pomjakushina, and T Shiroka. Multigap superconductivity in the mo5pb2 boron–phosphorus compound. New Journal of Physics, 22(9):093016, sep 2020.
[47] J Chen, L Jiao, J L Zhang, Y Chen, L Yang, M Nicklas, F Steglich, and H Q Yuan. Evidence for two-gap superconductivity in the non-centrosymmetric compound lanic2. New Journal of Physics, 15(5):053005, may 2013.
[48] N. R. Werthamer, E. Helfand, and P. C. Hohenberg. Temperature and purity dependence of the superconducting critical field, Hc2. iii. electron spin and spin-orbit effects. Phys. Rev., 147:295–302, Jul 1966.
[49] M. Tinkham. Effect of fluxoid quantization on transitions of superconducting films. Phys. Rev., 129:2413–2422, Mar 1963.
[50] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 9 - type ii superconductivity. In Charles P. Poole, Horacio A. Farach, and Richard J. Creswick, editors, Superconductivity, pages 265–311. Academic Press, 1995.