Vortex lines in a ferromagnetic spin-triplet superconductor

doi:10.1088/1674-1056/21/5/057401

Abstract Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of $\delta$ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of $\phi$-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a $\delta$ -like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.

Keywords: vortex lines spin-triplet superconductor topological current bifurcation

Received: 02 September 2011
Revised: 27 April 2012
Accepted manuscript online:

PACS:	74.20.-z	(Theories and models of superconducting state)
	74.25.Ha	(Magnetic properties including vortex structures and related phenomena)
	02.40.Pc	(General topology)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10905026 and 10905027), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20090211120030), and the Lanzhou Development of Science and Technology Program, China (Grant No. 2010-1-129).

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Zhao Li(赵力), Yang Jie(杨捷), Xie Qun-Ying(谢群英), Tian Miao(田苗), and Duan Yi-Shi(段一士) Vortex lines in a ferromagnetic spin-triplet superconductor 2012 Chin. Phys. B 21 057401

[1]	Niemi A J 2000 Phys. Rev. D 61 125006
[2]	Kibble T W B 1976 J. Phys. A 9 1387
[3]	Nelson D R and Toner J T 1981 Phys. Rev. B 24 363
[4]	Chen K, You Y X, Hu T Q, Zhu M H and Wang X Q 2011 Acta Phys. Sin. 60 024702 (in Chinese)
[5]	Lukyanchuk I A and Zhitomirsky M E 1995 Sup. Rev. 1 207
[6]	Volovik G E 2003 The Universe in a Helium Droplet (Oxford:Clarendon Press)
[7]	Volovik G E and Gor'kov L P 1984 Sov. Phys. JETP Lett. 39 647
[8]	Joynt R, Mineev V P, Volovik E G and Zhitomirsky M E 1990 Phys. Rev. B 42 2014
[9]	Zha G Q and Zhou S P 2010 Chin. Phys. B 19 027401
[10]	Mineev V P and Samokhin K V 1999 Introduction to Unconventional Superconductivity (Amsterdam:Gordon and Breach Science Publisher)
[11]	Yu H L, Peng J and Jin B X 2010 Chin. Phys. B 19 087203
[12]	Korshunov S 1985 Sov. Phys. JETP 62 301
[13]	Stein D L and Cross M C 1979 Phys. Rev. Lett. 42 504
[14]	Demler E and Zhou F 2002 Phys. Rev. Lett. 88 163001
[15]	Demler E, Nayak C and Das Sarma S 2001 Phys. Rev. Lett. 86 1853
[16]	Tou H, Kitaoka Y, Ishida K, Asayama K, Kimura N, Onuki Y, Yamamoto E, Haga Y and Maezawa K 1998 Phys. Rev. Lett. 80 3129
[17]	Ishida K, Mukuda H, Kitaoka Y, Asayama K, Mao Z Q, Mori Y and Maeno Y 1998 Nature 396 658
[18]	Knigavko A and Rosenstein B 1999 Phys. Rev. Lett. 82 1261
[19]	Pechenik E, Rosenstein B, Shapiro B Y and Shapiro I 2002 Phys. Rev. B 65 214532
[20]	Tokuyasu T A, Hess D W and Sauls J A 1990 Phys. Rev. B 41 8891.
[21]	Al Khawaja U and Stoof H 2001 Nature 411 918
[22]	Mizushima T, Machida K and Kita T 2002 Phys. Rev. Lett. 89 030401
[23]	Leonhardt V and Volovik G E 2000 JETP Lett. 72 46
[24]	Babaev E 2002 Phys. Rev. Lett. 88 177002
[25]	Faddeev L 1979 Einstein and Several Contemporary Tendencies in the Field Theory of Elementary Particles, Relativity, Quanta and Cosmology Vol. 1 (New York:Johnson Reprint Corporation)
[26]	Babaev E, Faddeev L D and Niemi A J 2002 Phys. Rev. B 65 100512
[27]	Ho T L 1998 Phys. Rev. Lett. 81 742
[28]	Mermin N D 1979 Rev. Mod. Phys. 51 591
[29]	Mäkelä H, Zhang Y and Suominen K A 2003 J. Phys. A 36 8555
[30]	Sornborger A, Carroll S M and Pyne T 1997 Phys. Rev. D 55 6454
[31]	Duan Y S 1984 The Structure of the Topological Current (No. SlAC-PUB-3301)
[32]	Duan Y S, Zhao L and Zhang X H 2006 Phys. Lett. A 360 183
[33]	Wu T T and Yang C N 1975 Phys. Rev. D 12 3845
[34]	Duan Y S and Ge M L 1979 Sci. Sin. 11 1072
[35]	Ren J R, Mo S F and Zhu T 2009 Chin. Phys. B 18 2901
[36]	Duan Y S, Fu L B and Jia G 2000 J. Math. Phys. 41 4379
[37]	Goursat É 1904 A Course in Mathematical Analysis (New York:Dover Publications)
[38]	Schouten J A 1951 Tensor Analysis for Physicists (Oxford:Clarendon Press)
[39]	Duan Y S and Zhang H 1999 Eur. Phys. J. D 5 47
[40]	Duan Y S, Wang J P, Liu X and Zhang P M 2003 Prog. Theor. Phys. 110 1

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Vortex lines in a ferromagnetic spin-triplet superconductor

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