Magnetic flux expulsion as collective vortex protection in the pair condensate
Above Tc — Normal
Below Tc — Superconducting
Why Pairs Expel Flux
The Cooper pairs' shared counter-rotating vortices are delicate structures. External co-rotating flow (magnetic field) would disrupt these seams.
The pairs collectively generate screening currents — cooperative flows that exactly cancel the external field within the bulk. Each pair is protecting its own shared vortex. The collective effect is macroscopic flux expulsion.
London Penetration Depth
λL = √(m/μ₀nse²) is the distance over which screening currents cancel the external field.
In substrate terms: the cooperative screening depth of the pair condensate. Higher pair density ns → shorter λL → more effective screening. For Nb: λL ≈ 39 nm. For YBCO: λL ≈ 150 nm.
What Screening Currents Are
Co-rotating substrate flows generated by the pair condensate, opposing the external field direction.
Not individual electron currents — collective response of the phase-locked condensate. The second London equation ∇×J = −(nse²/m)B relates the curl of these screening currents to the local field. This is the substrate's counter-rotating response to co-rotating perturbation.