Abrikosov Vortex Lattice — Type-II Superconductor

Flux Quantization & Vortex Physics

In a type-II superconductor between Hc1 and Hc2, magnetic flux penetrates as quantized vortices, each carrying exactly one flux quantum Φ₀ = h/2e ≈ 2.07×10⁻¹⁵ Wb.

The vortices form an Abrikosov triangular lattice (hexagonal packing) — minimizing the repulsive vortex-vortex interaction energy. Predicted 1957 by Abrikosov (Nobel 2003).

Each vortex has a normal core of size ξ (coherence length). Supercurrents circulate around it over scale λ (penetration depth). The ratio κ = λ/ξ > 1/√2 defines Type-II.

Φ₀ = h/2e — each vortex
B(r) = (Φ₀/2πλ²) K₀(r/λ)
Lattice: triangular, a = (2Φ₀/√3 B)^½