Vortex lines in a ferromagnetic spin-triplet superconductor

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

中国物理B ›› 2012, Vol. 21 ›› Issue (5): 57401-057401.doi: 10.1088/1674-1056/21/5/057401

Vortex lines in a ferromagnetic spin-triplet superconductor

赵力¹,杨捷¹,谢群英¹ ²,田苗³,段一士¹

1. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;
2. School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China;
3. School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730000, China

收稿日期:2011-09-02 修回日期:2012-04-27 出版日期:2012-04-01 发布日期:2012-04-01
基金资助:
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).

Vortex lines in a ferromagnetic spin-triplet superconductor

Zhao Li(赵力)^a)†, Yang Jie(杨捷)^a), Xie Qun-Ying(谢群英)^a)b), Tian Miao(田苗)^c), and Duan Yi-Shi(段一士)^a)

a. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;
b. School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China;
c. School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730000, China

Received:2011-09-02 Revised:2012-04-27 Online:2012-04-01 Published:2012-04-01
Supported by:
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).

摘要/Abstract

摘要： 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 δ 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 φ-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 δ-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.

关键词: vortex lines, spin-triplet superconductor, topological current, bifurcation

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.

Key words: vortex lines, spin-triplet superconductor, topological current, bifurcation

中图分类号: (Theories and models of superconducting state)

74.20.-z

74.25.Ha (Magnetic properties including vortex structures and related phenomena) 02.40.Pc (General topology)

赵力, 杨捷, 谢群英, 田苗, 段一士. Vortex lines in a ferromagnetic spin-triplet superconductor[J]. 中国物理B, 2012, 21(5): 57401-057401.

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[J]. Chin. Phys. B, 2012, 21(5): 57401-057401.

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Vortex lines in a ferromagnetic spin-triplet superconductor

Vortex lines in a ferromagnetic spin-triplet superconductor

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