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)

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).

[4]. Yong-Jihn Kim,

[5]. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B

[6]. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B

[7]. A. A. Abrikosov and L. P. Gor’kov, Phys. Rev. B

[8]. Yong-Jihn Kim and A. W. Overhauser, Phys. Rev. B