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Nucleation of bulk superconductivity close to critical magnetic fields

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  • Department of Mathematical Sciences
We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field HC2 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.
Original languageEnglish
JournalAdvances in Mathematics
Volume226
Issue2
Pages (from-to)1213-1258
Number of pages46
ISSN0001-8708
DOIs
Publication statusPublished - 2011

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