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Vitaly Lazarevich Ginzburg and Lev Landau applied an order parameter description to superconductivity in 1950. A spatially varying complex amplitude extends the fixed-amplitude description of the London equations. Their initial charge assumption preceded the later identification of the universal pair charge.^[ref]

Consider the following isotropic, local SI Helmholtz free energy model near a continuous superconducting transition temperature:Here $\beta >0$, $m_{\ast }>0$ is a phenomenological mass parameter, and $q=-2e$ fixes the electron-pair convention. The uniform superconducting minimum for $\alpha <0$ has $|{\psi }_0{|}^2=-\alpha /\beta$. The gradient term penalizes changes of the amplitude and the gauge-invariant quantum phase; the magnetic term penalizes magnetic field penetration. The gauge-coupling sign in Ginzburg-Landau superconductivity keeps the electric current and field equation consistent. This model omits material anisotropy, microscopic nonlocality and critical fluctuations.

Awarded in equal thirds to Alexei Alexeyevich Abrikosov, Vitaly Lazarevich Ginzburg and Anthony J. Leggett for pioneering theoretical contributions to superconductors and superfluids.^[ref]