Sorry guys I really don't understand the idea of vortex in superconductor, why superconductors type II have vortices ?
Thanks in advance!
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If you use the Ginzburg-Landau theory for superconductivity you obtain two length scales:
Depending on the ratio between this two lengths ($\kappa = \lambda/\xi$) it will be energetically favourable or not to create superconductor-normal conductor interfaces when increasing the applied magnetic field. Therefore we have two types of superconductors:
You can check Wikipedia for more details: https://en.wikipedia.org/wiki/Ginzburg%E2%80%93Landau_theory