-
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:
- holographic superconductor /
- Lifshitz black hole /
- coherence length /
- magnetic penetration depth
[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
-
[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
Catalog
Metrics
- Abstract views: 6524
- PDF Downloads: 205
- Cited By: 0
下载:
