Lifshitz时空s波超导模型的关联长度和穿透深度

杨卓群; 吴亚波; 鲁军旺; 张成园; 张雪

doi:10.7498/aps.65.040401

摘要

在D=d+2维各向异性的Lifshitz黑洞时空背景中, 在探子极限下, 用解析方法研究了临界温度附近引力系统的微扰, 计算出超导的关联长度(1/Tc)(1-(T/Tc)-1/2, 这与平均场论的结果一致. 进一步, 考虑在该系统中加一个均匀外磁场, 计算出穿透深度(Tc-T)-1/2, 该结果与Ginzburg-Landau理论相符.

关键词:

The AdS/CFT duality provides us a powerful guidance to study the strong-coupled conformal field theory by using its dual weak-coupled gravity. One of the interesting applications of the duality is to study high temperature superconductors, which are supposed to be a strongly coupled system. According to Ginzburg-Landau theory, a superconductor can be characterized by only two parameters, coherence length and the magnetic penetration length ; therefore, it is important to determine the two parameters. In this paper in the D=d+2-dimensional Lifshitz black hole, we analytically study the static fluctuation of the scalar field with nonzero spatial momentum along one spatial coordinate of the boundary, and investigate the perturbation of the gravitational system near the critical temperature Tc. Working in the probe limit (the gauge field and scalar field do not backreact on the original metric), we obtain the superconducting coherence length via AdS/CFT (anti-de Sitter/conformal field theory) correspondence, which is (1/Tc)(1-(T/Tc)-1/2. Moreover, in the probe limit (the magnetic field does not backreact to the background spacetime), we have calculated the diamagnetic current induced by a homogeneous external magnetic field perpendicular to the surface of the superconductor. Then, we obtain the magnetic penetration depth (Tc-T)-1/2, which agrees with the result in Ginzburg-Landau theory. And these results strongly support the idea that a superconductor can be described by a charged scalar field on the Lifshitz black hole via AdS/CFT (anti-de Sitter/conformal field theory) duality.

Keywords:

作者及机构信息

1.
辽宁师范大学物理与电子技术学院, 大连 116029;

2.
黔南民族师范学院物理与电子科学系, 都匀 558000

通信作者: 吴亚波, ybwu61@163.com

基金项目: 国家自然科学基金(批准号: 11175077, 11575075)资助的课题.

Authors and contacts

1.
School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China;

2.
Department of Physics, Qiannan Normal College for Nationalities, Duyun 558000, China

Corresponding author: Wu Ya-Bo, ybwu61@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11175077, 11575075).

参考文献

[1]	Bekenstein J D 1973 Phys. Rev. D 7 2333
[2]	Hawking S W 1975 Commun. Math. Phys. 43 199
[3]	Hooft G T 1993 arXiv:gr-qc/9310026
[4]	Susskind L 1995 J. Math. Phys. 36 6377
[5]	Maldacena J M 1999 Int. J. Theor. Phys. 38 1113
[6]	Witten E 1998 Adv. Theor. Math. Phys. 2 253
[7]	Gubser S S, Klebanov I R, Polyakov A M 1998 Phys. Lett. B 428 105
[8]	Hartnoll S A, Herzog C P, Horowitz G T 2008 Phys. Rev. Lett. 101 031601
[9]	Maeda K, Okamura T 2008 Phys. Rev. D 78 106006
[10]	Gubser S S, Pufu S S 2008 J. High Energy Phys. 11 033
[11]	Cai R G, Li L, Li L F 2014 J. High Energy Phys. 01 032
[12]	Chen J W, Kao Y J, Maity D, Wen W Y, Yeh C P 2010 Phys. Rev. D 81 106008
[13]	Cai R G, He S, Li L, Li L F 2013 J. High Energy Phys. 12 036
[14]	Nie Z Y, Cai R G, Gao X, Zeng H 2013 J. High Energy Phys. 11 087
[15]	Horowitz G T, Roberts M M 2008 Phys. Rev. D 78 126008
[16]	Cai R G, Li L F, Wang Y Q 2013 J. High Energy Phys. 09 074
[17]	Cai R G, Nie Z Y and Zhang H Q 2010 Phys. Rev. D 82 066007
[18]	Ling Y, Niu C, Wu J P, Xian Z Y, Zhang H B 2014 Phys. Rev. Lett. 113 091602
[19]	Zeng X X, Liu X M, Liu W B 2014 J. High Energy Phys. 03 031
[20]	Wu Y B, Lu J W, Zhang C Y, Zhang N, Zhang X, Yang Z Q, Wu S Y 2015 Phys. Lett. B 741 138
[21]	Wu Y B, Lu J W, Liu M L, Lu J B, Zhang C Y, Yang Z Q 2014 Phys. Rev. D 89 106006
[22]	Nakonieczny L, Rogatko M 2014 Phys. Rev. D 90 106004
[23]	Nakonieczny L, Rogatko M, Wysokinski K 2015 Phys. Rev. D 92 066008
[24]	Franco S, Garcia-Garcia A M, Rodriguez-Gomez D 2010 J. High Energy Phys. 04 092
[25]	Rogatko M, Wysokinski K 2015 arXiv:1510.06137[hep-th]
[26]	Chen S B, Pan Q Y, JIng J L 2012 Chin. Phys. B 21 040403
[27]	Peng Y, Deng F A, Liu G H, Yang K F 2015 Acta Phys. Sin. 64 157401 (in Chinese) [彭严, 邓方安, 刘国华, 杨凯凡 2015 64 157401]
[28]	Kachru S, Liu X, Mulligan M 2008 Phys. Rev. D 78 106005
[29]	Lu J W, Wu Y B, Qian P, Zhao Y Y, Zhang X, Zhang N 2014 Nucl. Phys. B 887 112
[30]	Taylor M 2008 arXiv:0812.0530[hep-th]
[31]	Pang D W 2014 Commun. Theor. Phys. 62 265

施引文献

[1]	Bekenstein J D 1973 Phys. Rev. D 7 2333
[2]	Hawking S W 1975 Commun. Math. Phys. 43 199
[3]	Hooft G T 1993 arXiv:gr-qc/9310026
[4]	Susskind L 1995 J. Math. Phys. 36 6377
[5]	Maldacena J M 1999 Int. J. Theor. Phys. 38 1113
[6]	Witten E 1998 Adv. Theor. Math. Phys. 2 253
[7]	Gubser S S, Klebanov I R, Polyakov A M 1998 Phys. Lett. B 428 105
[8]	Hartnoll S A, Herzog C P, Horowitz G T 2008 Phys. Rev. Lett. 101 031601
[9]	Maeda K, Okamura T 2008 Phys. Rev. D 78 106006
[10]	Gubser S S, Pufu S S 2008 J. High Energy Phys. 11 033
[11]	Cai R G, Li L, Li L F 2014 J. High Energy Phys. 01 032
[12]	Chen J W, Kao Y J, Maity D, Wen W Y, Yeh C P 2010 Phys. Rev. D 81 106008
[13]	Cai R G, He S, Li L, Li L F 2013 J. High Energy Phys. 12 036
[14]	Nie Z Y, Cai R G, Gao X, Zeng H 2013 J. High Energy Phys. 11 087
[15]	Horowitz G T, Roberts M M 2008 Phys. Rev. D 78 126008
[16]	Cai R G, Li L F, Wang Y Q 2013 J. High Energy Phys. 09 074
[17]	Cai R G, Nie Z Y and Zhang H Q 2010 Phys. Rev. D 82 066007
[18]	Ling Y, Niu C, Wu J P, Xian Z Y, Zhang H B 2014 Phys. Rev. Lett. 113 091602
[19]	Zeng X X, Liu X M, Liu W B 2014 J. High Energy Phys. 03 031
[20]	Wu Y B, Lu J W, Zhang C Y, Zhang N, Zhang X, Yang Z Q, Wu S Y 2015 Phys. Lett. B 741 138
[21]	Wu Y B, Lu J W, Liu M L, Lu J B, Zhang C Y, Yang Z Q 2014 Phys. Rev. D 89 106006
[22]	Nakonieczny L, Rogatko M 2014 Phys. Rev. D 90 106004
[23]	Nakonieczny L, Rogatko M, Wysokinski K 2015 Phys. Rev. D 92 066008
[24]	Franco S, Garcia-Garcia A M, Rodriguez-Gomez D 2010 J. High Energy Phys. 04 092
[25]	Rogatko M, Wysokinski K 2015 arXiv:1510.06137[hep-th]
[26]	Chen S B, Pan Q Y, JIng J L 2012 Chin. Phys. B 21 040403
[27]	Peng Y, Deng F A, Liu G H, Yang K F 2015 Acta Phys. Sin. 64 157401 (in Chinese) [彭严, 邓方安, 刘国华, 杨凯凡 2015 64 157401]
[28]	Kachru S, Liu X, Mulligan M 2008 Phys. Rev. D 78 106005
[29]	Lu J W, Wu Y B, Qian P, Zhao Y Y, Zhang X, Zhang N 2014 Nucl. Phys. B 887 112
[30]	Taylor M 2008 arXiv:0812.0530[hep-th]
[31]	Pang D W 2014 Commun. Theor. Phys. 62 265

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