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M. Fairbank, Phys. Rev. Lett. 7, 43 (1961). 17. L. MeMilan, Phys. Rev. 167,331 (1968). 18. B. Allen In: Dynamical Properties of Solids, Vol. 3, 95, Ed. K. Horton et ai, (North Holland, Amsterdam 1980); G. Bergmann and D. Rainer, Z. Physik 263, 59 (1973). 19. D. Osheroff, RC. M . Lee, Phys. Rev. Lett. H. B. Ketterson, Edts, published by John Wiley and Sons, New York (1978). 20. F. R Sehrieffer, Phys. Rev. Lett. 17,433 (1966); Phys. Rev . B 30, 1408 (1966). 21. L. Degiorgi, Rev. Mod. Phys. 71,687 (1999); F.

The above derivation of the London equation is subject to some restrictions. 43) for the superconducting current is valid only under some conditions. First of all, the magnetic field must be weak compared to the critical field He. Further, the equation is valid only if all quantities, the current density for example, vary sufficiently slowly in space. 3 below). 51) the magnetic induction, and consequently the current, change on the scale of the penetration depth. Thus, we obtain the condition J »~o .

One may speculate what would have happened if this surprising observation had been achieved before the discovery of the high Tc- cuprates. In Fig. 23 the structure of MgB 2 is shown. H. Bennemann. B. Ketterson (a) 10 5 AFM IIII .... ; 1 f\ 24 28 32 P (khar) 20 Q. 21. Superconductivity in Heavy-Fermion systems: (a) Typical complex phase diagram, (b) Pressure induced superconductivity. (Here, TN refers to the Neel temperature, TSG to the spin-glass temperature, NFL to nearly Fermi-liquid behavior, and p to the electrical resistivity) in particular to low energy phonons and to the E 2g - mode at Wo ~ 67 me V involving B-B vibrations.