低溫比熱是一個研究塊材樣品之物理性質的一個有力工具。對於超導性而言，低溫比熱可以探索超導體的配對態，在磁場下也能提供額外的資訊。在此篇論文中，我們進行了YNi2B2C，NbSe2，和CeRu2超導體在磁場下詳細的比熱研究。(1)YNi2B2C單晶在轉變溫度約等於13.77 K時被發現有超導現象。而其超導電子比熱可以用點節點(point-node)或雙能隙模型來描述。(2) NbSe2單晶具有二維的晶體結構，超導溫度約為6.7 K。而臨界磁場的各項異性，也就是臨界磁場在磁場垂直c軸和平行c軸的比值約為3。我們利用雙能隙模型探討了超導電子比熱和電子比熱隨磁場的關係。得到的擬合參數，比如能隙大小和大小能隙間的相對比例，在兩者(Ce和γ)的分析是吻合的，表示NbSe2的超導性可以用雙能隙的模型來描述。(3)最後，我們研究了多晶CeRu2在不同磁場下的直流磁化率和比熱特性。在此塊材樣品中，可能的雜項或奈米叢集的量在經過熱處理後被減少了。根據零磁場和磁場下的比熱數據分析可知，CeRu2是一個具有各項異性能隙的BCS類型超導體。

Low temperature specific heat (LTSH) is a powerful tool to investigate the physical properties of bulk samples. For superconductivity, LTSH can probe the pairing state in superconductors and provides additional information under magnetic fields. In this thesis, I present comprehensive specific-heat studies of superconductivity in YNi2B2C, NbSe2, and CeRu2. (1) Single crystalline YNi2B2C was found to be superconducting at the superconducting transition temperature Tc ~ 13.77 K. The superconducting specific heat Ce(T) can be described by either the point-node or the two-gap model. (2) Single crystalline NbSe2 has a two-dimensional crystalline structure showing the Tc ~ 6.7 K and the anisotropy in the critical fields, Hc2⊥/Hc2// ~3. We investigated the Ce(T) and the electronic specific heat γ(H) by the two-gap model. Obtained fitting parameters, such as gap values and the relative ratio of two gaps in both analyses (Ce(T) and γ(H)), are comparable meaning that the superconductivity of NbSe2 can be described by the two-gap scenario. (3) Finally, we studied the DC magnetic susceptibility and the specific heat of polycrystalline CeRu2 in different magnetic fields. In the bulk CeRu2, the amount of the possible impurity phase or nano-clusters was reduced after annealing. Based on the analysis results of zero-field and in-field specific heat, CeRu2 is a BCS-like superconductor with an anisotropic gap.

Abstract (English)…………………………...…………………………………………...I
Abstract (Chinese)………………………………………………………………...…….II
Content…………………..………………………………………………….....…..........III
Chapter 1: Introduction…………………..…..………….…………......................1
1.1 History of superconductivity…………………………………...........….........…..1
1.2 Two-gap superconductor………………………...………...........…….…......…..5
1.3 Motivation…………………………...…………………………...….............…...8
Chapter 2: Experimental instruments…………………..…………...…….…..9
2.1 Relaxation-method calorimeter………………………………………...….….....9
2.1.1 3He refrigerator…...…………………….……………….…….……….….9
2.1.2 Relaxation-method calorimeter (RMC)……………….………………….11
I. Basic principle………………………………………………….……..11
II. Hardware of RMC……………………………………..…….………..12
III. Software of RMC…………….…………….………………………….16
2.2 Magnetic Properties Measurement System (MPMS, Quantum Design)………..20
2.2.1 Temperature control………………...…………………………………….20
2.2.2 Superconducting magnet…………………………...……………………..23
2.2.3 Longitudinal and transverse coils…………………….………………….24
2.2.4 Reciprocating sample option (RSO)…………………………………….26
2.3 Adiabatic-method calorimeter (AMC)……………………………………..…28
Chapter 3: Theory………………………………………………...……………….29
3.1 BCS theory………………………………………………….…………………..29
3.2 Specific heat of matter at low temperatures……………………………………35
3.2.1 Lattice specific heat………………………………………………………35
I. Dulong-Petit law…………….……...…………………………………35
II. Quantum theory of specific heat…….…………………..…………….36
III. Einstein model………………………………………………………38
IV. Debye model…………………….....……………….....……………....39
3.2.2 Electronic specific heat……………......….………....………..…………..44
3.2.3 Superconducting electronic specific heat in different order parameters....45
Chapter 4: Results and analysis…………………………..………………..…..49
4.1 A possible point-node or two-gap superconductor: YNi2B2C…………………..49
4.2 A two-gap superconductor: NbSe2….……………………………...…………...60
4.3 A BCS-like superconductor CeRu2 with an anisotropic gap……………………75
Chapter 5: Conclusion………………………………………………….……..….90
Appendix: High pressure calorimeter (HPC) operation manual………98
References……………………………………..………………….………………...109
Publication list……………………………….…………………..…………...…...117

1. H. Kamerlingh Onne, Leiden comm., 120b, 122b, 124c (1911).
2. J. Bardeen, L. N. Copper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
3. G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1986).
4. J. W. Chen, S. E. Lambert, M. B. Maple, Z. Fisk, J. L. Smith, G. R. Stewart, and J. O. Willis, Phys. Rev. B 30, 1583 (1984).
5. R. J. Cava, H. Takagi, H. W. Zandbergen, J. J. Krajewski, W. F. Peck, T. Siegrist, B. Batlogg, R. B. Vandover, R. J. Felder, K. Mizuhashi, J. O. Lee, H. Eisaki, and U. Uchida, Nature (London) 367, 252 (1994).
6. K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian, and T. Sasaki, Nature 422, 53 (2003).
7. Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz, and F. Lichtenberg, Nature 372, 532 (1994).
8. J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Nature (London) 410, 63 (2001).
9. C. P. Sun, J. –Y. Lin, S. Mollah, P. L. Ho, H. D. Yang, F. C. Hsu, Y. C. Liao, and M. K. Wu, Phys. Rev. B 70, 054519 (2004).
10. P. Szado, P. Samuely, J. Dačmarčík, T. Klein, J. Marcus, D. Fruchart, S. Miraglia, C. Marcenat, and A. G. M. Jansen, Phys. Rev. Lett. 87, 137005 (2001).
11. X. K. Chen, M. J. Konstantinovic, and J. C. Irwin, D. D. Lawrie, and J. P. Franck, Phys. Rev. Lett. 87, 157002 (2001).
12. F. Bouquet, Y. Wang, R. A. Fisher, D. G. Hinks, J. D. Jorgensen, A. Junod, and N. E. Philips, Europhys. Lett. 56, 856 (2001).
13. H. J. Choi, D. Roundy, H. Sun, M. L. Cohen, and S. G. Louie, Nature 418, 758 (2002).
14. M. Tinkham, Introduction to Superconductivity 2nd edition, McGraw-Hill Inc. (1996).
15. L. N. Cooper, Phys. Rev. 104, 1189 (1956).
16. A. Tari, The Specific Heat of Matter at Low Temperatures, Imperial College Press. (2003).
17. Y. Sun and K. Maki, Phys. Rev. B 51, 6059 (1995).
18. R. Nagarajan, C. Mazumdar, Z. Hossain, S. K. Dhar, K. V. Gopalakrishnan, L. C. Gupta, C. Godart, B. D. Padalia, R. Vijayaraghavan, Phys. Rev. Lett. 72, 274 (1994).
19. L. F. Mattheiss, Phys. Rev. B 49, 13279(R) (1994).
20. K. –H. Muller and V. N. Narozhnyi, Rep. Prog. Phys. 64, 943 (2001), and references cited therein.
21. B. H. Brandow, Philos. Mag. 83, 2487 (2003).
22. S. A. Carter, B. Batlogg, R. J. Cava, J. J. Krajewski, W. F. Peck, Jr., and H. Takagi, Phys. Rev. B 50, 4216(R) (1994).
23. H. Michor, T. Holubar, C. Dusek, and G. Hilscher, Phys. Rev. B 52, 16165 (1995).
24. R. S. Gonnelli, A. Morello, G. A. Ummarino, V. A. Stepanov, G. Behr, G. Graw, S. V. Shulga, and S. L. Drechsler, Int. J. Mod. Phys. B 14, 2840 (2000).
25. M. Nohara, H. Suzuki, N. Mangkorntong, and H. Takagi, Physica C 341-348, 2177 (2000).
26. I. S. Yang, M. V. Klein, S. L. Cooper, P. C. Canfield, B. K. Cho, and S. –I. Lee, Phys. Rev. B 62, 1291 (2000).
27. K. Izawa, A. Shibata, Y. Matsuda, Y. Kato, H. Takeya, K. Hirata, C. J. van der Beek, and M. Konczykowski, Phys. Rev. Lett. 86, 1327 (2001).
28. K. Izawa, K. Kamata, Y. Nakajima, Y. Matsuda, T. Watanabe, M. Nohara, H. Takagi, P. Thalmeier, and K. Maki, Phys. Rev. Lett. 89, 137006 (2002).
29. E. Boaknin, R. W. Hill, C. Proust, C. Lupien, L. Taillefer, and P. C. Canfield, Phys. Rev. Lett. 87, 237001 (2001).
30. Y. Matsuda and K. Izawa, Physica C 388-389, 487 (2003).
31. T. Park, M. B. Salamon, E. M. Choi, H. J. Kim, and S. I. Lee, Phys. Rev. Lett. 90, 177001 (2003).
32. T. Park, E. E. M. Chia, M. B. Salamon, E. Bauer, I. Vekhter, J. D. Thompson, E. M. Choi, H. J. Kim, S. I. Lee, and P. C. Canfield, Phys. Rev. Lett. 92, 237002 (2004).
33. P. Raychaudhuri, D. Jaiswal-Nagar, G. Sheet, S. Ramakrishnan, and H. Takeya, Phys. Rev. Lett. 93, 156802 (2004).
34. T. Watanabe, M. Nohara, T. Hanaguri, and H. Takagi, Phys. Rev. Lett. 92, 147002 (2004).
35. H. Nishimori, K. Uchiyama, S. Kaneko, A, Tokura, H. Takeya, K. Hirata, and N. Nishida, J. Phys. Soc. Jpn. 73, 3247 (2004).
36. M. Nohara, M. Isshiki, H. Takagi, and R. J. Cava, J. Phys. Soc. Jpn. 66, 1888 (1997).
37. M. Nohara, M. Isshiki, F. Sakai, and H. Takagi, J. Phys. Soc. Jpn. 68, 1078 (1999).
38. G. Wang and K. Maki, Phys. Rev. B 58, 6493 (1998).
39. K. J. Song, C. Park, S. S. Oh, Y. K. Kwon, J. R. Thompson, D. G. Mandrus, D. McK. Paul, and C. V. Tomy, Physica C 398, 107 (2003).
40. K. Maki, P. Thalmeier, and H. Won, Phys. Rev. B 65, 140502(R) (2002).
41. Q. Yuan and P. Thalmeier, Phys. Rev. B 68, 174501 (2003).
42. Q. Yuan, H. Y. Chen, H. Won, S. Lee, K. Maki, P. Thalmeier, and C. S. Ting, Phys. Rev. B 68, 174510 (2003).
43. H. Doh, M. Sigrist, B. K. Cho, and S. –I. Lee, Phys. Rev. Lett. 83, 5350 (1999).
44. S. V. Shulga, S. –L. Drechsler, G. Fuchs, K. –H. Muller, K. Winzer, M. Heinecke, and K. Krug, Phys. Rev. Lett. 80, 1730 (1998).
45. S. Muhhopadhyay, G. Sheet, P. Raychaudhuri, and H. Takeya, Phys. Rev. B 72, 014545 (2005).
46. D. L. Bashlakov, Y. G. Naidyuk, I. K. Yanson, S. G. Wimbush, B. Holzapfel, G. Fuch, and S. L. Drechsler, Supercond. Sci. Technol. 18, 1094 (2005).
47. B. K. Cho, P. C. Canfield, L. L. Miller, D. C. Johnston, W. P. Beyermann, and A. Yatskar, Phys. Rev. B 52, 3684 (1995).
48. S. J. Chen, C. F. Chang, H. L. Tsay, H. D. Yang, and J. –Y. Lin, Phys. Rev. B 58, 14753(R) (1998).
49. H. D. Yang, J. –Y. Lin, H. H. Li, F. H. Hsu, C. J. Liu, S. –C. Li, R. –C. Yu, and C. –Q. Jin, Phys. Rev. Lett. 87, 167003 (2001).
50. F. Bouquet, R. A. Fisher, N. E. Phillips, D. G. Hinks, and J. D. Jorgensen, Phys. Rev. Lett. 87, 47001 (2001).
51. K. A. Moler, D. L. Sisson, J. S. Urbach, M. R. Beasley, A. Kapitulnik, D. J. Baar, R. Liang, and W. N. Hardy, Phys. Rev. B 55, 3954 (1997).
52. G. E. Volovik, JETP Lett. 58, 469 (1993).
53. F. Bouquet, Y. Wang, I. Sheikin, T. Plackowski, A. Junod, S. Lee, and S. Tajima, Phys. Rev. Lett. 89, 257001 (2002).
54. N. Nakai, M. Ichioka, and K. Machida, J. Phys. Soc. Jpn. 71, 23 (2002).
55. L. Lyard, P. Samuely, P. Szabo, T. Klein, C. Marcenat, L. Paulius, K. H. P. Kim, C. U. Jung, H. –S. Lee, B. Kang, S. Choi, S. –I. Lee, J. Marcus, S. Blanchard, A. G. M. Jansen, U. Welp, G. Karapetrov, and W. K. Kwok, Phys. Rev. B 66, 180502(R) (2002).
56. M. D. Johannes, I. I. Mazin, and C. A. Howells, Phys. Rev. B 73, 205102 (2006).
57. B. T. Matthias, T. H. Geballe, and V. B. Compton, Rev. Mod. Phys. 35, 1 (1963).
58. E. Revolinsky, E. P. Lautenschlager, and C. H. Armitage, Solid State Commun. 1, 59 (1963).
59. A. Wilson, F. J. Di Salvo, and Mahajan, Phys. Rev. Lett. 32, 882 (1974).
60. E. Boaknin, M. A. Tanatar, J. Paglione, D. Hawthorn, F. Ronning, R. W. Hill, M. Sutherland, L. Taillefer, J. Sonier, S. M. Hayden, and J. W. Brill, Phys. Rev. Lett. 90, 117003 (2003).
61. H. Suderow, V. G. Tissen, J. P. Brison, J. L. Martinez, and S. Vieira, Phys. Rev. Lett. 95, 117006 (2005).
62. J. M. E. Harper, T. H. Geballe, and F. J. DiSalvo, Phys. Rev. B 15, 2943 (1977).
63. A. H. Castro Neto, Phys. Rev. Lett. 86, 4382 (2001).
64. H. D. Yang and J.-Y. Lin, J. Phys. Chem. Solid 62, 1861 (2001) and references therein.
65. H. F. Hess, R. B. Robinson, and J. V. Waszczak, Phys. Rev. Lett. 64, 2711 (1990).
66. R. Corcoran, P. Meeson, Y. Onuki, P-A. Probst, M. Springford, K. Takita, H. Harima, G. Y. Guo, and B. L. Gyorffy, J. Phys.: Condens. Matter 6, 4479 (1994).
67. D. Sanchez, A. Junod, J. Muller, H. Berger, and F. Levy, Physica B 204, 167 (1995).
68. J. E. Sonier, M. F. Hundley, J. D. Thompson, and J. W. Brill, Phys. Rev. Lett. 82, 4914 (1999).
69. T. Yokoya, T. Kiss, A.Chainani, S. Shin, M. Nohara, H. Takagi, Science 294, 2518 (2001). T. Valla, A. V. Fedorov, P. D. Johnson, P-A. Glans, C. McGuinness, K. E. Smith, E. Y. Andrei, and H. Berger, Phys. Rev. Lett. 92, 086401 (2004).
70. K. Rossnagel, O. Seifarth, L. Kipp, M. Skibowski, D. Voss, P. Krüger, A. Mazur, and J. Pollmann, Phys. Rev. B 64, 235119 (2001).
71. T. Hanaguri, A. Koizumi, K. Takaki, M. Nohara, H. Takagi, and K. Kitazawa, Physica B 329-333, 1355 (2003).
72. J. D. Fletcher, A. Carrington, P. Diener, P. Rodière, J. P. Brison, R. Prozorov, T. Olheiser, and R. W. Giannetta, Phys. Rev. Lett. 98, 57003 (2007).
73. H. F. Hess, R. B. Robinson, and J. V. Waszczak, Physica B 169, 422 (1991).
74. J. G. Rodrigo and S. Vieira. Physica C 404, 306 (2004).
75. V. Barzykin and L. P. Gor’kov, Phys. Rev. Lett. 98, 087004 (2007).
76. R. Bel, K. Behnia, and H. Berger, Phys. Rev. Lett. 91, 066602 (2003).
77. C. L. Huang, J.-Y. Lin, C. P. Sun, T. K. Lee, J. D. Kim, E. M. Choi, S. I. Lee, and H. D. Yang, Phys. Rev. B 73, 012502 (2006).
78. V. Guritanu, W. Goldacker, F. Bouquet, Y. Wang, R. Lortz, G. Goll, and A. Junod, Phys. Rev. B 70, 184526 (2004).
79. A. L. Carr, J. J. Trafton, S. Dukan, and Z. Tešanovic, Phys. Rev. B 68, 174519 (2003).
80. N. Nakai, P. Miranovic, M. Ichioka, and K. Machida, Phys. Rev. B 70, 100503(R) (2004).
81. A. P. Ramirez, Phys. Lett. A 211, 59 (1996).
82. J.-Y. Lin, P. L. Ho, H. L. Huang, P. H. Lin, Y. –L. Zhang, R. -C. Yu, C. –Q. Jin, and H. D. Yang, Phys. Rev. B 67, 052501 (2003).
83. V. A. Sirenko, N. I. Makedonska, Yu. A. Shabakayeva, and R. Shleser, Low Temp. Phys. 28, 574 (2002).
84. A. V. Sologubenko, I. L. Landau, H. R. Ott, A. Bilusic, A. Smontara, and H. Berger, Phys. Rev. Lett. 91, 197005 (2003).
85. B. T. Matthias, H. Suhl, and E. Corenzwit, Phys. Rev. Lett. 1, 449 (1958).
86. K. Yagasaki, M. Hedo, and T. Nakama, J. Phys. Soc. Jpn, 62, 3825 (1993).
87. A. D. Huxley, C. Paulsen, O. Laborde, J. L. Tholence, D. Sanchez, A. Junod, and R. Calemczuk, J. Phys. Cond. Matter 5, 3825 (1993).
88. K. Matsuda, Y. Kohori, and T. Kohara, J. Phys. Soc. Jpn. 64, 2750 (1995).
89. H. Mukuda, K. Ishida, Y. Kitaoka, and K. Asayama, J. Phys. Soc. Jpn. 67, 2101 (1998).
90. M. Hedo, Y. Inada, E. Yamamoto, Y. Haga, Y. Onuki, Y. Aoki, T. D. Matsuda, H. Sato, and S. Takahashi, J. Phys. Soc. Jpn. 67, 272 (1998).
91. R. R. Joseph, K. A. Gschneidner, Jr., and, D. C. Koskimaki, Phys. Rev. B 6, 3286 (1972).
92. A. D. Huxley, C. Paulsen, O. Laborde, J. L. Tholence, D. Sanchez, A. Junod, and R. Calemczuk, J. Phys.: Condens. Matter 5, 7709 (1993).
93. 洪大軒，Master Thesis, Fu Jen Catholic University (2004).
94. N. T. Panousis and K. A. Gschneidner, Jr., Phys. Rev. B 5, 4767 (1972).
95. C. Kittel, “Introduction to Solid State Physics” 7th edition, p 124 (1996).
96. V. N. Smolyaninova, K. Ghosh, and R. L. Greene, Phys Rev. B 58, R14725 (1998).
97. T. Suzuki, H. Goshima, S. Sakita, T. Fujita, M. Hedo, Y. Inada, E. Yamamoto, Y. Haga, and Y. Onuki, Physica B 230-232, 176 (1997).
98. K. Ishida, H. Mukuda, Y. Kitaoka, K. Asayama, and Y. Onuki, Z. Naturforsh. 51a, 793 (1996).
99. T. Sakakibara, A. Yamada, J. Custers, K. Yano, T. Tayama, H. Aoki, and K. Machida, J. Phys. Soc. Jpn. 76, 051004 (2007).
100. Y. Y. Chen, private communication.
101. A. Palenzona, J. Alloys and Compounds 176, 241 (1991).
102. W. –H. Li, C. C. Yang, F. C. Tsao, S. Y. Wu, P. J. Huang, M. K. Chung, and Y. D. Yao, Phys. Rev. B 72, 214516 (2005).
103. V. Guritanu, W. Goldacker, F. Bouquet, Y. Wang, R. Lortz, G. Goll, and A. Junod, Phy. Rev. B 70, 184526 (2004).
104. J. S. Kim, R. K. Kremer, L. Boeri, and F. S. Razavi, Phys. Rev. Lett. 96, 217002 (2006).
105. Y. Taguchi, M. Hisakabe, and Y. Iwasa, Phys. Rev. Lett. 94, 217002 (2005).
106. Y. Nakajima, T. Nakagawa, T. Tamegai, and H. Harima, Phys. Rev. Lett. 100, 157001 (2008).
107. G. Mu, H. Luo, Z. Wang, L. Shan, C. Ren, and H. H. Wen, Phys. Rev. B 79, 174501 (2009).