Type I vs Type II Superconductors

How the ratio κ = λ_L / ξ determines whether flux is excluded or penetrates as quantized vortices

κ = λ_L / ξ 0.50 Type I

κ = 0.1 ← Type I · Type II → κ = 2.0

Length Scale Cross-Section

Complete Flux Exclusion

Screening currents / λ_L

Counter-rotating vortex / ξ

External magnetic flux

Superconducting bulk

Why This Type

ξ > λ_L — The pair vortex is spatially larger than the screening depth. A flux line would need to penetrate a region smaller than the pair to enter — but doing so would rupture the vortex, destroying the pair. The condensate excludes all flux until the field overwhelms it at a single critical field H_c.

Examples

Type I: Pb (κ ≈ 0.48), Hg (κ ≈ 0.15), Sn (κ ≈ 0.15), Al (κ ≈ 0.01)

Type II: Nb (κ ≈ 1.1), NbTi (κ ≈ 60), YBCO (κ ≈ 95)