Explain Abrikosov vortex lattice in superconductors.
The vortex lattice, as described in my 1957 work and elaborated upon in my Nobel lecture, is a direct consequence of the behavior of type-II superconductors when subjected to a magnetic field exceeding a certain critical value, Hc1. Unlike type-I superconductors, which expel magnetic fields entirely up to Hc, type-II materials allow the magnetic flux to penetrate. However, this penetration is not uniform. It occurs in discrete, quantized flux tubes, or vortices. Each vortex carries a single quantum of magnetic flux, Φ₀ = h/2e. These vortices arrange themselves into an ordered, periodic array, a lattice, due to the minimization of the system's free energy. This orderly structure is fundamental to understanding their high critical fields.
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