The first, lower critical field occurs when magnetic flux vortices penetrate the material but the material remains superconducting outside of these microscopic vortices.
2.
Type II superconductors allow a different sort of mixed state, where the magnetic field ( above the lower critical field H _ { c1 } ) is allowed to penetrate along cylindrical " holes " through the material, each of which carries a magnetic flux quantum.
3.
Abrikosov vortices can be trapped in a type-II superconductor by chance, on defects, etc . Even if initially type-II superconductor contains no vortices, and one applies a magnetic field H larger than the lower critical field H _ { c1 } ( but smaller than the upper critical field H _ { c2 } ), the field penetrates into superconductor in terms of "'Abrikosov vortices " '.
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