BCS ↔ Substrate Glossary

Every BCS parameter has a substrate equivalent — standard formula on the left, physical rendering on the right

Δ

Energy Gap

BCS: 2Δ = 3.53 k_BT_c (weak coupling)

Standard

2Δ(0) = 3.53 k_BT_c

Nb: Δ ≈ 1.5 meV
Tc = 9.3 K

Substrate

Energy in the shared
counter-rotating seam

ξ

Coherence Length

BCS: ξ = ℏv_F / (πΔ)

Standard

ℏv_F / (πΔ)

ℏ = diffusivity (C2)
v_F = Fermi velocity
Δ = vortex energy

[J·s × m/s / J] = m ✓

Substrate

Distance traveled at v_F
in one vortex oscillation

λ_L

London Penetration Depth

London: λ_L = √(m / μ₀n_se²)

Standard

√(m / μ₀n_se²)

m = electron mass (C4)
n_s = pair density
Nb: λ_L ≈ 39 nm

Substrate

Cooperative screening
depth of pair condensate

κ

Ginzburg-Landau Parameter

GL: κ = λ_L / ξ — determines flux behavior

Standard

κ = λ_L / ξ

κ < 1/√2 → Type I
κ = 1/√2 → boundary
κ > 1/√2 → Type II

[m / m] = dimensionless ✓

Substrate

Vortex extent vs
screening depth ratio