Abrikosov Vortex

An Abrikosov vortex is a topological defect in a type-II superconductor — a quantized filament of magnetic flux that penetrates the superconducting condensate when the applied field exceeds the lower critical field H_c1. Each vortex carries exactly one quantum of magnetic flux, Φ₀ = h/2e ≈ 2.07 × 10⁻¹⁵ Wb, and consists of a normal-conducting core surrounded by circulating supercurrents that screen the magnetic field over the London penetration depth.

The vortex was predicted theoretically by Alexei Abrikosov in 1957, extending the Ginzburg-Landau theory of superconductivity to the type-II regime where the Ginzburg-Landau parameter κ > 1/√2. In this regime, the energy cost of forming a normal core is outweighed by the gain in magnetic energy, and the material admits a mixed state with numerous vortices arranged in a hexagonal lattice — the Abrikosov lattice — that minimizes their mutual repulsion.

The Abrikosov vortex is the condensed-matter realization of a flux tube: a topologically protected configuration of gauge field and order parameter that cannot be removed by local perturbations without destroying the superconducting state itself. Its quantized flux is a direct consequence of the macroscopic phase coherence of the superconducting order parameter, and the requirement that this phase be single-valued around any closed loop. The vortex is not merely a magnetic disturbance; it is a topological knot in the superconducting wavefunction.

The Abrikosov lattice is often presented as a solved problem — a textbook exercise in mean-field theory. This is a mistake. The vortex lattice is a non-equilibrium structure that forms under drive, adapts to disorder, and melts through a sequence of phase transitions that are still not fully understood. Treating it as a static crystal misses the essential physics: a lattice of topological defects in a broken-symmetry medium is a paradigm for how structure emerges from competing interactions, and its relevance extends far beyond superconductivity to any system where order competes with frustration.