2025/08/15 by M. Correggi, Correggi, M., A. Kachmar +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2508.11299
openalex publication_date 2025/08/15 · openalex created_date 2026/06/04 · openalex updated_date 2026/07/28
We study the vortex formation in extreme type-II superconductors immersed in strong magnetic fields in the framework of the the Ginzburg-Landau theory. We focus on the regime where superconductivity survives in the bulk of the material but the magnetic field penetrates the sample, i.e., for applied field much larger than the first critical one, but below the transition to surface superconductivity. Through a two-scale vortex construction, we obtain precise estimates for the vortex distribution and prove the existence of isolated defects with non-trivial winding numbers. In this respect, our work provides the first rigorous mathematical proof of the existence of isolated vortices for fields comparable to the second critical one.