在這論文中，我們利用格林函數方法對鐵基高溫超導體的配對對稱性做一理論上的研究。我們計算在三種目前被提出的配對對稱性下的自旋響應函數，關聯至非彈性中子散射實驗。在我們的結果中顯示出無論是在電子或電洞掺雜下，s± 波的能隙形式是與近期的中子散射實驗結果最為吻合，並且在論文的最後簡單的給出在考慮Hund’s 耦合的頂角修正項，在任何配對對稱性下，響應函數的共振行為都會隨著耦合強度增強而有劇烈的改變。

Superconductivity is an important research subject in condensed-matter physics. In last 20s years, the copper-based high-temperature superconductors (HTSC), called the cuprates, have been discovered and many subsequent studies have been done. However, there remains some unsolved subtlety, such as the superconducting mechanism and the pairing symmetry. In January of last year, the iron-based HTSC were discovered, and many scientists believed that these new type of HTSC might hold the key to solve problems of HTSC as mentioned previously. In this thesis, we present a theoretical study of pairing symmetry of iron-based HTSC (e.g. LaFxO1-xFeAs) by the Green’s function method. There are several candidates of the pairing symmetry proposed, to which we calculated the spin response for three types of gap function (i.e. s±, extended-s, and dx2 - y2 wave). It is found that the s± wave is most favored in either electron or hole doping and it agrees well with recent inelastic neutron scattering experiments. Moreover, we have also studied the effect of Hund’s coupling through the random-phase approximation vertex correction

[1] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).
[2] H. Takahashi, K. Igawa, K. Arii, Y. Kamihara, M. Hirano, and H.Hosono, Nature 453, 376 (2008).
[3] C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff II, J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo, N. L. Wang, and P. Dai, Nature 453, 899 (2008).
[4] Michael R. Norman, Physics 1, 21 (2008)
[5] J. Dong, H. J. Zhang, G. Xu, Z. Li, G. Li, W. Z. Hu, D. Wu, G. F. Chen, X. Dai, J. L. Luo, Z. Fang, and N. L. Wang, Europhys. Lett. 83, 27006 (2008).
[6] T. Nomura, S. W. Kim, Y. Kamihara, M. Hirano, P. V. Sushko, K. Kato, M. Takata, A. L. Shluger, and H. Hosono, arXiv:0804.3569.
[7] W. E. Pickett, Rev. Mod. Phys. 61, 433 (1989).
[8] I. I. Mazin, M. D. Johannes, L. Boeri, K. Koepernik, and D. J. Singh, Phys. Rev. B 78, 085104 (2008).
[9] D. J. Singh and M-H. Du, Phys. Rev. Lett. 100, 237003 (2008); D. J. Singh, arXiv:0807.2643.
[10] I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Phys. Rev. Lett. 101, 057003 (2008)
[11] S. Raghu, Xiao-Liang Qi, Chao-Xing Liu, D. J. Scalapino, and Shou-Cheng Zhang, Phys. Rev. B 77, 220503 (2008)
[12] J. Dong et al., Europhys. Lett. 83, 27006 (2008)
[13] C. de la Cruz et al., Nature (London) 453, 899 (2008)
[14] J. P. Lu, Phys. Rev. Lett 68, 125 (1992)
[15] K. Seo, B. A. Bernevig, and J. Hu, Phys. Rev. Lett 101, 206404 (2008)
[16] I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Phys. Rev. Lett 101, 057003
(2008)
[17] C. Fang, H. Yao, W. –F. Tsai, J. Hu, and S. A. Kivelson, Phys. Rev. B 77, 224509
(2008)
[18] Q. Si and E. Abrahams, arXiv：0804.2480 (2008)
[19] K. Nakayama, T. Sato, P. Richard, Y. –M. Xu, Y. Sekiba, S. Souma, G. F. Chen, J. L.
Luo, N. L. Wang, H. Ding, and T. Takahashi, arXiv：0812.0663 (2008)
[20] T. A. Maier and D. J. Scalapino, Phys. Rev. B 78, 020514 (2008)
[21] P. A. Lee and X. -G. Wen, arXiv: 0804.1739 (2008).
[22] T. A. Maier, S. Graser, D. J. Scalapino, and P. Hirschfeld, Phys. Rev. B 79, 134520
(2009)
[23] S. –L Yu, J. Kang, J. -X Li, Phys. Rev. B 79, 064517 (2009)
[24] M. M. Korshunov, I. Eremin, Phys. Rev. B 78, 140509 (2008)
[25] I. Schnell et al.,Phys. Rev. B 68, 245102 (2003)