Ginzburg-Landau Theory

superconductor · vortices · coherence length

κ = 0.50
H/H_c = 0.30
T/T_c = 0.50
Physics: GL free energy: F = α|ψ|² + β|ψ|⁴ + (1/2m*)|(-iℏ∇−e*A)ψ|² + B²/2μ₀. Coherence length ξ = ℏ/√(−2m*α), penetration depth λ = √(m*/μ₀e*²|ψ₀|²); GL parameter κ = λ/ξ. Type I (κ < 1/√2 ≈ 0.707): complete Meissner effect, Pb (κ≈0.4), Hg. Type II (κ > 1/√2): mixed state between H_c1 and H_c2 where Abrikosov vortices penetrate; each vortex carries one flux quantum Φ₀ = h/2e = 2.07×10⁻¹⁵ Wb. NbTi (κ≈12), YBCO (κ≈100) are Type II; high-T_c superconductors all Type II.