Engineering & Science
Ginzburg-Landau Parameter (κ) & Upper Critical Field (B_c2) Formula
Calculate the Ginzburg-Landau ratio κ = λ_L / ξ_GL, classify Type-I vs. Type-II Abrikosov vortex superconductors across κ = 1/SQRT(2), and compute upper critical field B_c2 = SQRT(2) * κ * B_c.
Why Alexei Abrikosov’s κ = 1/√2 = 0.7071 boundary makes MRI & fusion magnets possible!
Pure elemental superconductors like aluminum (λ_L = 50 nm, ξ_GL = 1,600 nm -> κ = 0.0313) expel magnetic flux completely (Meissner state) until they quench abruptly at tiny thermodynamic critical fields (~10 mT). Using Vitaly Ginzburg and Lev Landau’s 1950 order-parameter theory, Alexei Abrikosov (1957 Nobel-winning discovery) proved that whenever the London penetration depth λ_L exceeds coherence length ξ_GL by κ = λ_L / ξ_GL > 1 / SQRT(2) ≈ 0.7071, surface energy flips negative—allowing quantized Φ_0 magnetic flux vortices to thread the bulk up to an enormous upper critical field B_c2 = SQRT(2) * κ * B_c!
Look at A15 Nb_3Sn superconducting magnet wire (λ_L = 85 nm, ξ_GL = 3.5 nm, thermodynamic critical field B_c = 0.52 T): κ = 85 / 3.5 = 24.29 >> 0.7071 ("Type-II Abrikosov Vortex Superconductor"), boosting upper critical field 34.3× up to B_c2 = SQRT(2) * (85 / 3.5) * 0.52 = 17.86 Tesla!
| Superconductor (λ_L & ξ_GL) | GL Parameter κ = λ_L / ξ_GL | Abrikosov Criterion vs 0.7071 | Upper Critical Field B_c2 |
|---|---|---|---|
| Nb3Sn Magnet Wire (λ=85 nm, ξ=3.5 nm, Bc=0.52 T) | 24.29 | κ > 1/√2 -> Type-II Vortex State | 17.86 Tesla |
| Pure Aluminum (λ=50 nm, ξ=1600 nm, Bc=0.01 T) | 0.0313 | κ < 1/√2 -> Type-I Meissner Only | Quenches at Bc = 0.01 T |
| Invalid Length <= 0 | Error Guard | "Invalid Length Inputs" | Positivity Check |
Ginzburg-Landau Parameter κ = λ_L / ξ_GL & Type-II Upper Critical Field B_c2 (T)
Computes B_c2 = SQRT(2) * (λ_L / ξ_GL) * B_c when κ > 1/SQRT(2), or flags Type-I Meissner behavior where B_c itself limits superconductivity.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Superconductor Inputs", IF((B2 / B3) > (1 / SQRT(2)), ROUND(SQRT(2) * (B2 / B3) * B4, 2), "Type-I Superconductor (Quenches at Bc)"))Dimensionless Ginzburg-Landau Ratio κ = λ_L / ξ_GL
Divides London penetration depth B2 (nm) by Ginzburg-Landau coherence length B3 (nm).
=IF(OR(B2 <= 0, B3 <= 0), "Invalid Superconductor Inputs", ROUND(B2 / B3, 4))Try the example
Use the original values or change them to test your understanding.