Derivation of Lower Critical Magnetic Field for Anisotropic Ginzburg-Landau Model in Superconductivity

• Published in: Acta mathematica Sinica. English series Vol. 27; no. 5; pp. 953 - 982
• Main Authors: Kou, Yan Lei, Ding, Shi Jin
• Format: Journal Article
• Language: English
• Published: Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.05.2011; Springer Nature B.V
• Subjects: Anisotropy; Asymptotic properties; Boundary conditions; Coordinate transformations; Energy; Fluid flow; Landau; Magnetic fields; Mathematical models; Mathematics; Mathematics and Statistics; Phase transitions; Studies; Superconductivity; Thin films; Vortices; 临界磁场; 十六进制; 各向异性参数; 旋涡结构; 渐近行为; 超导模型; 超导薄膜; Critical magnetic field; vortices; anisotropic Ginzburg-Landau model; 35Q40; 35J55
• ISSN: 1439-8516; 1439-7617
• DOI: 10.1007/s10114-011-8206-z

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field Hc1 which is the first critical value of hex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter k, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.