Theory 07/Superconductivity

Critical Field Is a Ratio of Lengths

The claim

The upper critical field of a disordered superconductor is set by the ratio of coherence length to mean free path rather than by coherence length alone.

01The mechanism

Impurities shorten both the coherence length and the mean free path; the field at which vortices overlap depends on how the two shrink together.

02Predictions

P1Critical field should collapse onto the ratio.
P2Clean and dirty samples should differ.

03Refutation

Critical field tracking coherence length alone would remove the ratio.