Existence of Bulk Vortices in Superconductors with Strong Magnetic Fields

Michele Correggi (Politecnico Milano)

Nov 27. 2025, 14:00 — 14:40

We review the phenomenon of nucleation of vortice in a type-II superconductor immersed in an external magnetic field in the framework of the the Ginzburg-Landau theory. We discuss the phase transitions occurring in the sample as the intensity of the field grows and focus on the regime close but below the second critical field, where superconductivity survives in the bulk of the material but the magnetic field penetrates the sample. 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.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Many-body Systems and Bose-Einstein Condensation: A Mathematical Physics Perspective (Workshop)
Organizer(s):
Serena Cenatiempo (Gran Sasso Science Institute, L'Aquila)
Christian Hainzl (LMU Munich)
Robert Seiringer (ISTA, Klosterneuburg)