Abstract
Nonmagnetic impurities change the electron-phonon interaction in a metal and therefore they influence the superconducting properties. This is demonstrated for an impure simple metal by deriving the Eliashberg equation. It turns out that (1) this equation is of the same formal structure as in the clean case, (2) there exists an additional coupling of low-frequency transverse phonons to the electrons, whereas (3) the interaction between longitudinal phonons and electrons is reduced. Since the former effect is much larger than the latter, the effective phonon density of states α2 F(ω) is considerably enlarged in the low-frequency regime, which generally leads to an increased transition temperature and energy gap. Calculated values of the change in the transition temperature are compared for various impurity concentrations with experimental results and satisfactory agreement is obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Abrikosov and L. P. Gor'kov,Soviet Phys.—JETP 12, 1243 (1961).
P. W. Anderson,J. Phys. Chem. Solids 11, 26 (1959).
T. Tsuneto,Prog. Theor. Phys. 28, 5, 857 (1962).
W. Buckel and R. Hilsch,Z. Physik 132, 420 (1952).
W. Buckel and R. Hilsch,Z. Physik 138, 109 (1954).
G. von Minnigerode,Z. Physik 154, 442 (1959).
E. StriederAnn. Physik 22, 15 (1968).
G. von Minnigerode and J. Rothenberg,Z. Physik 213, 397 (1968).
K. Knorr and N. Barth,Solid State Commun. 6, 791 (1968).
G. Bergmann,Z. Physik 228, 25 (1969).
G. Ziemba and G. Bergmann,Z. Physik 237, 410 (1970).
A. Comberg and S. Ewert,Z. Physik 268, 241 (1974).
A. Comberg, S. Ewert, and G. Bergmann,Z. Physik 271, 317 (1974).
J. D. Leslie, J. T. Chen and T. T. Chen,Can. J. Phys. 48, 2783 (1970).
N. V. Zavaritskii,Soviet Phys.—JETP 30, 412 (1970).
H. Wühl, J. E. Jackson, and C. V. Briscoe,Phys. Rev. Lett. 20, 1496 (1968).
K. Knorr and N. Barth,J. Low Temp. Phys. 4, 469 (1971).
J. W. Garland, K. H. Bennemann and F. M. Müller,Phys. Rev. Lett. 21, 1315 (1968).
G. Bergmann,Phys. Rev. B 3, 3797 (1971).
S. Ewert,Z. Physik 237, 47 (1970).
Ch. Ohlerich and W. Buckel,Phys. Verh. 6, 683 (1972).
S. Ewert,Z. Physik 267, 283 (1974).
H. Wühl, S. Ewert, and A. Comberg,Verhandl. DPG (VI) 10, 626 (1975).
A. Comberg, S. Ewert, and H. Wühl, to be published.
J. Bolz and F. Pobell,Verhandl. DPG (VI) 10, 626 (1975).
T. Tsuneto,Phys. Rev. 121, 402 (1961).
A. Schmid,Z. Physik 259, 421 (1973).
L. J. Sham and J. M. Ziman,Solid State Physics, Vol. 15 (Academic Press, New York, 1963), p. 223.
J. A. Reissland,The Physics of Phonons (Wiley, New York, 1973), Chapter 8, p. 256.
A. B. Pippard,Phil. Mag. 46, 1104 (1955).
E. Eisenriegler,Z. Physik 258, 185 (1973).
G. Grünewald and K. Scharnberg,Z. Physik 268, 197 (1974).
A. A. Abrikosov, L. P. Gor'kov, I. Ye. Dzyaloshinski,Quantum Field Theoretical Methods in Statistical Physics (Prentice-Hall, 1963), § 39.
G. Bergmann and D. Rainer,Z. Physik 263, 59 (1973).
B. Keck and A. Schmid,Solid State Comm. 17, 799 (1975).
Author information
Authors and Affiliations
Additional information
We are indebted to the Deutsche Forschungsgemeinschaft for the financial support of this work.
Rights and permissions
About this article
Cite this article
Keck, B., Schmid, A. Superconductivity and electron-phonon interaction in impure simple metals. J Low Temp Phys 24, 611–629 (1976). https://doi.org/10.1007/BF00657170
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00657170