Nucleation of bulk superconductivity close to critical magnetic field

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• 作者：S&#xf8 ; ren Fournais ; Ayman Kachmar
• 关键词：Ginzburg– ; Landau functional ; Elliptic estimates ; Variational methods ; Thermodynamic limits ; Magnetic Schr&#xf6 ; dinger operators
• 刊名：Advances in Mathematics
• 出版年：2011
• 出版时间：30 January 2011
• 年：2011
• 卷：226
• 期：2
• 页码：1213-1258
• 全文大小：317 K

文摘

We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field H_C2 and large Ginzburg–Landau parameter, we provide leading order estimates on the energy of minimizing configurations. We obtain a fine threshold value of the applied magnetic field for which bulk superconductivity contributes to the leading order of the energy. Furthermore, the energy of the bulk is related to that of the Abrikosov problem in a periodic lattice. A key ingredient of the proof is a novel L^∞-bound which is of independent interest.