On the GLAG (Ginzburg-Landau-Abrikosov-Gor’kov) theory

From O. Madelung’s Introduction to Solid-State Theory (Springer-Verlag, Berlin, 1978).

P. 251

● Phenomenological Ginzburg-Landau theory

From, M. Tinkham’s Introduction to Superconductivity (McGraw-Hill, New York, 1996)

The Ginzburg-Landau theory was not well accepted, until Gor'kov showed that
his Green's function formalism leads to the GL theory near Tc [1].

● However, Gor’kov’s microscopic derivation [1] 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.

[1]. L. P. Gor'kov, Sov. Phys. JETP, 9, 1364(1959).
[2]. Yong-Jihn Kim Pairing constraint on the real space formalism of the theory of superconductivity ,
invited talk at APCTP Inauguration Conference (1996).
[3]. Yong-Jihn Kim, A Constraint on the Anomalous Green’s function, Mod. Phys. Lett.B 10, 555 (1996).
[4]. Yong-Jihn Kim, Pairing in the Bogoliubov-de Gennes equations, Int. J. Mod. Phys. B 11, 1731 (1997).
[5]. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B 47, 8025 (1993).
[6]. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B 49, 12339 (1994).
[7]. A. A. Abrikosov and L. P. Gor’kov, Phys. Rev. B 49, 12337 (1994).
[8]. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B 49, 15799 (1994).