Abrikosov-Gorkov theory

We start from the Abrikosov-Gorkov theory and its predictions for Tc. In that theory the effect of the randomly distributed magnetic scattering centers of concentration m is characterized by a pair-breaking parameter o which is given by... 

The difference to the Abrikosov-Gorkov theory are much less pronounced if the ground state is a Kramers doublet or more generally a degenerate state which is magnetic. For details we refer to Keller and Fulde (1971). 

Fig. 17.23. Jump in the specific heat 4C as function of TJT for the system La,.,Pr Sn3. The solid line represents the theoretical curve which does not contain any fit parameter. Also shown for comparison is the result of the Abrikosov-Gorkov theory (AG) (from McCalium et al., 1975).

Although the Abrikosov-Gorkov theory has been quite successful in explaining many of the effects of well-defined magnetic impurities, some experimental results are not explainable by theory and have been discussed by Sugawara. ° ... 

A. L. Fetter, J. D. Walecka, Quantum Theory ofMany-Particle systems (McGraw-Hill, New York, 1971) A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinski, Methods of Quantum field Theory in Statistical Mechanics (Dover, New York, 1975). 

Nozieres, P. Theory of interacting fermi systems. New York Benjamin 1964 Abrikosov, A., Gorkov, L., Dzyaloshinski, J. Methods of quantum field theory in statistical physics. Englewood Cliffs Prentice-Hall 1963... 

Abrikosov A.A., Gorkov L.P., Dzyaloshinskii I.E. (1998) Metody kvantovoi teorii polya v statisticheskoi fizike (Methods of the quantum theory of a field in statistical physics). Moscow Dobrosvet. 514 p. 

I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevskii, "The general theory of van der Waals forces," Adv. Phys., 10, 165 (1961), for the method, though applied only to a vacuum gap see also Chapter VIII, E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics, Part 2 in Vol. 9 of Course of Theoretical Physics Series (Pergamon, Oxford, 1991) a systematic derivation of the full DLP result is given also in Chap. 6 of A. A. Abrikosov, L. P. Gorkov, Sc I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, R. A. Silverman, trans. (Dover, New York, 1963). 

Abrikosov, A. A., Gorkov, L. P., Dzyaloshinskii, I. E. Methods of Quantum Field Theory in Statistical Physics, Dover Publications Inc., New York 1975... 

Fig. 17.13. TJT as function of the pair-breaking parameter a a as predicted by the theory of Abrikosov and Gorkov (1960).

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