On the GLAG (Ginzburg-Landau-Abrikosov-Goríkov)
From O. Madelungís Introduction to Solid-State Theory (Springer-Verlag, Berlin, 1978).
● Phenomenological Ginzburg-Landau theory
From, M. Tinkhamís Introduction to Superconductivity (McGraw-Hill, New York, 1996)
The Ginzburg-Landau theory was not well accepted, until Gor'kov showed that
● However, Goríkovís microscopic derivation  of the Ginzburg-Landau theory is not valid!
The problem is in using the self-consistency equation which violates the
physical constraint of the Anomalous Green's function [2,3,4,5,6,7,8].
The gradient term may not be derived microscopically, because the local free energy density is not well defined for the Cooper pairs
as for the hard-core particles.
=> Corrected self-consistency equation:
where P denotes the pairing constraint derived from the physical constraint of the system.
. L. P. Gor'kov, Sov.
Phys. JETP, 9, 1364(1959).
. Yong-Jihn Kim†† Pairing constraint on the real space formalism of the theory of superconductivity ,
invited talk at APCTP Inauguration Conference (1996).
. Yong-Jihn Kim, A Constraint on the Anomalous Greenís function, Mod. Phys. Lett.B 10, 555 (1996).
. Yong-Jihn Kim, Pairing in the Bogoliubov-de Gennes equations, Int. J. Mod. Phys. B 11, 1731 (1997).
. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B 47, 8025 (1993).
. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B 49, 12339 (1994).
. A. A. Abrikosov and L. P. Goríkov, Phys. Rev. B 49, 12337 (1994).
. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B 49, 15799 (1994).