Ginzburg–Landau theory

A phenomenological theory of superconductivity that describes the superconducting state with a complex order parameter and its spatial variations.

Ginzburg–Landau free energy: A phenomenological free-energy functional whose minimum determines the superconducting order parameter and electromagnetic response. Its competing terms set the magnitude and spatial variation of the superconducting state.
Superconductivity: A state of matter with zero electrical resistance and distinctive magnetic behavior below a critical temperature. Ginzburg–Landau theory is a macroscopic description of this state.
Vitaly Ginzburg: A Soviet theoretical physicist who helped develop the phenomenological theory of superconductivity bearing his name. His work with Landau established the theory in 1950.
Type-II superconductor: A superconductor that allows magnetic flux to penetrate in quantized vortices above a lower critical field. The Ginzburg–Landau parameter identifies this class when its value exceeds the critical threshold.
London theory: A phenomenological theory describing electromagnetic fields and currents in superconductors. London theory captures magnetic screening but lacks a spatially varying order parameter.
Ginzburg–Landau parameter: The ratio of the magnetic penetration depth to the coherence length in a superconductor. It determines whether magnetic flux is expelled or enters as vortices.
Order parameter: A quantity that characterizes the degree of order in a physical system. The complex order parameter distinguishes the superconducting phase from the normal state.
Lev Landau: A Soviet physicist whose work on phase transitions and condensed matter shaped twentieth-century theoretical physics. He co-authored the superconductivity theory with Ginzburg.
Upper critical field: The magnetic field above which superconductivity is destroyed in a material. The theory predicts how superconductivity disappears under strong applied fields.
Fluctuation theory: The study of deviations from average behavior that become significant near phase transitions. Mean-field Ginzburg–Landau predictions can fail when order-parameter fluctuations grow strong.

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