Abrikosov Vortex Lattice in Type-II Superconductors

Magnetic flux tubes arrange into a triangular lattice — Nobel Prize 2003 (Abrikosov)

Controls

Superconductor

5.0
0.40
0.30

Dynamics

0.05
0

State

Vortex count (Nv)
Lattice typeTriangular
Flux per vortexΦ₀

Physics

Type-II superconductors (κ > 1/√2) allow partial flux penetration as quantized vortices. Each carries exactly Φ₀ = h/2e.
κ = λ_L / ξ_GL
fᵢⱼ = (Φ₀²/4πμ₀λ²) K₁(rᵢⱼ/λ)
Vortex repulsion (London interaction) + boundary conditions → Abrikosov triangular lattice minimizes free energy.