In physics, Ginzburg-Landau theory is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity. Instead, it examines the macroscopic properties of a superconductor with the aid of general thermodynamic arguments.
Based on Landau's previously-established theory of second-order phase transitions, Landau and Ginzburg argued that the free energy F of a superconductor near the superconducting transition can be expressed in terms of a complex order parameter ψ, which describes how deep into the superconducting phase the system is. The free energy has the form
The Ginzburg-Landau equations produce many interesting and valid results. Perhaps the most important of these is its prediction of the existence of two characteristic lengths in a superconductor. The first is a coherence length ξ, given by
The ratio κ = λ/ξ is known as the Ginzburg-Landau Parameter. It has been shown that Type I superconductors are those with κ < 1/√2, and Type II superconductors those with κ > 1/√2.
The most important finding from Ginzburg-Landau theory was made by Alexei Abrikosov in 1957. In a type-II superconductor in a high magnetic field - the field penetrates in quantized tubes of flux, which are most commonly arranged in a hexagonal arrangement.
This theory arises as the scaling limit of the XY model.