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Meissner Effect for Type-II Superconductors

I was wondering whether the breakdown field strength for the Meissner effect may be attributed to the Zeeman effect? I can see the latter (along with the Stark effect) to be more analogous to electron screening but would the effect on the density of states due to the reduction of degeneracy have any correlation to the critical field strength that puts a type II superconductor into the phase with quantized vortices?