Linear and Nonlinear Electron Transport in Solids pp 239-274 | Cite as

# Structural Effects on Superconductivity

Chapter

## Abstract

The aim of the article is to discuss some aspects of the effects of structure and structural transformations of solids on their superconductive properties.

## Keywords

Structural Effect Superconducting Transition Temperature Tungsten Bronze Surface Plasmon Mode Soft Phonon
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## References

- 1.V. L. Ginzburg, Usp. Fiz. Nauk 101, 185 (1970).ADSCrossRefGoogle Scholar
- 1a.V. L. Ginzburg, Sov. Phys. - Usp. 13, 335 (1970)MathSciNetADSCrossRefGoogle Scholar
- 2.V. L. Ginzburg and D. A. Kirzhnits, in Soviet-American Symposium on Electron Theory of Solids, Leningrad, 1971 (unpublished).Google Scholar
- 3.D. Allender, J. Bray and J. Bardeen, Phys. Rev. B7, 1020 (1973).ADSCrossRefGoogle Scholar
- 4.J. C. Inkson and P. W. Anderson, Phys. Rev. Comments and Addenda B8, 4429 (1973).ADSCrossRefGoogle Scholar
- 5.D. Allender, J. Bray and J. Bardeen, ibid, p. 4434.Google Scholar
- 6.A. D. Wadsley in “Non-Stoichiometric Compounds”, L. Mandelcorn, ed., Academic Press, New York (1964).Google Scholar
- 7.C. J. Raub, A. R. Sweedler, M. A. Jensen, S. Broadsten and B. T. Matthias, Phys. Rev. Letters 13, 746 (1964)ADSCrossRefGoogle Scholar
- 7a.A. R. Sweedler, C. J. Raub and B. T. Matthias, Phys. Letters 15, 108 (1965)ADSCrossRefGoogle Scholar
- 7b.J. P. Remeika, T. H. Geballe, B. T. Matthias, A. S. Cooper, G. W. Hall and E. M. Kelly, Phys. Letters 24A, 565 (1967).ADSCrossRefGoogle Scholar
- 8.H. R. Shanks, Solid State Commun. 15, 753 (1974).ADSCrossRefGoogle Scholar
- 9.B. C. Hyde and M. O’Keefe, Acta Cryst. A29, 243 (1973).CrossRefGoogle Scholar
- 10.P. W. Anderson, B. I. Halperin and C. Varma, Phil. Mag. 25, 1 (1972).ADSMATHCrossRefGoogle Scholar
- 11.W. Cochran, Adv. Phys. 9, 387 (1960)ADSCrossRefGoogle Scholar
- 11a.P. W. Anderson, Fiz Dielect, G. I. Skanawi, ed., Academy of Sciences, Moscow (1960).Google Scholar
- 12.M. H. Cohen and D. H. Douglass, Jr., Phys. Rev. Letters 19, 118 (1967).ADSCrossRefGoogle Scholar
- 13.P. W. Anderson in Proceedings of the NATO Advanced Study Institute on Elementary Excitations in Atoms, Molecules and Solids, Antwerp, Belgium (1973).Google Scholar
- 14.H. Frohlich, J. Phys. C1, 544 (1968).ADSGoogle Scholar
- 15.H. Gutfreund and Y. Unna, J. Phys. Chem. Solids 34, 1523 (1973).ADSCrossRefGoogle Scholar
- 16.A. Rothwarf, Phys. Rev. B2, 3560 (1970).ADSCrossRefGoogle Scholar
- 17.For a review see E. N. Economou and K. L. Ngai, to appear as a chapter in “Advances in Chemical Physics”, edited by S. A. Rice and I. Prigogine, John Wiley and Sons, New York (1974).Google Scholar
- 18.E. N. Economou, Phys. Rev. 182, 539 (1969).ADSCrossRefGoogle Scholar
- 19.J. C. Swihart, J. App l. Phys, 32, 461 (1961).ADSCrossRefGoogle Scholar
- 20.K. L. Ngai, Phys. Rev. 182, 555 (1969).ADSCrossRefGoogle Scholar
- 21.K. L. Ngai and E. N. Economou, unpublished.Google Scholar
- 22.P. Morel and P. W. Anderson, Phys. Rev. 125 , 1263 (1962).ADSCrossRefGoogle Scholar
- 23.A. L. Fetter, to be published.Google Scholar
- 24.E. N. Economou, Phys. Rev. 182, 539 (1969).ADSCrossRefGoogle Scholar
- 25.x (Q, w) does not depend on a because in the RPA x depends only on the electronic eigenenergy E = h2Q2 which is independent on a.
_{Qa}2mGoogle Scholar - 26.F. Stern, Phys. Rev. Letters 18, 546 (1967).CrossRefGoogle Scholar
- 27.W. L. McMillan, Phys. Rev. 167, 331 (1968).ADSCrossRefGoogle Scholar
- 28.The quantity λ is expected to change as we go from the bulk to a very thin film structure. Consequently, a calculation of T
_{c}in a given layered material requires the calculation of λ for this layered structure as well as the calculation of μ.Google Scholar - 29.C. C. Tsuei and W. L. Johnson, Phys. Rev. B9, 4742 (1974).ADSCrossRefGoogle Scholar
- 30.G. Deutscher, J. P. Farges, F. Meunier and P. Nedellec, Phys. Letters 35A, 265 (1971).ADSCrossRefGoogle Scholar
- 31.K. L. Ngai and E. N. Economou, Phys. Rev. B4, 2132 (1971)ADSCrossRefGoogle Scholar
- 31a.K. L. Ngai, E. N. Economou and Morrel H. Cohen, Phys. Rev. Letters 24, 61 (1970).ADSCrossRefGoogle Scholar
- 32.K. L. Ngai, E. N. Economou and Morrel H. Cohen, Phys. Rev. Letters 22, 1375 (1969).ADSCrossRefGoogle Scholar
- 33.A. J. Bevolo, H. R. Shanks, P. H. Sidles and G. C. Danielson, Phys. Rev. B9, 3220 (1974).ADSCrossRefGoogle Scholar
- 34.J. C. Slater, “Quantum Theory of Molecules and Solids”, Vol. 2, McGraw Hill, New York (1965).MATHGoogle Scholar
- 35.H. R. Shanks, Jour. Cryst. Growth 13/14, 433 (1972).CrossRefGoogle Scholar
- 36.Since the triangular tunnels are too small to contain M atoms, the Tl configuration has available per unit cell one square tunnel and four pentagonal ones, whereas T2 has nine squares. The outer tunnels are shared with other unit cells, so the ratio becomes 3:5, hence xm
_{ax}(T1) =. 6.Google Scholar - 37.The hexagonal phase consists of only triangular and hexagonal tunnels (see Ref. 6, p. 139), and thus cannot be derived geometrically from T2 in the same manner as Tl. The free energy arguments made in the text are nonetheless valid for this phase.Google Scholar
- 38.Eq. (4) assumes uncorrelated behavior of the M atoms. We note that a linear dependence of w
^{2}on x has been observed for a TO phonon in the nons to ichiometric f erro electric PZT by G. Burns and B. A. Scott, Phys. Rev. Letters 25, 1191 (1970), as described in A. Pinczuk, Solid State Comm. 12, 1035 (1973).ADSCrossRefGoogle Scholar - 39.Contributions from all possible configurational paths between Tl and T2, or from all combinations of phases of rotating groups of WO6 octahedra, are included in the tunneling matrix element V (x).Google Scholar
- 40.A. A. Abrikosov, L. P. Gorkov and I. E. Dzyaloshinskii, “Quantum Field Theoretical Methods in Statistical Physics”, second edition, Pergamon, New York (1965).MATHGoogle Scholar
- 41.W. L. McMillan, Phys. Rev. 167, 331 (1968). The general form of this equation can be derived analytically from the Eliashberg gap equations, although to obtain the constants numerical calculations based on the phonon spectrum of Nb were used. The results obtained in thispaper do not depend on the exact values of these constants.ADSCrossRefGoogle Scholar
- 42.D. J. Scalapino in “Superconductivity”, R. D. Parks, ed., Dekker, New York (1969).Google Scholar
- 43.In Ref. 8 it is pointed out that specific heat measurements on cubic Na W0 yield N(0) proportional to x, and that preliminary susceptibility measurements in the Tl phase of Na
_{x}WO3 give the same result. In a rigid band model this would require an extremely rapid variation of N(E) vs. E.Google Scholar - 44.Preliminary data on T
_{c}(x) in the hexagonal phase for K_{x}WO_{3}and Rb_{x}WO3 suggests behavior of the type shown in Fig. 6(b), H. R. Shanks and M. J. Sienko, private communications.Google Scholar - 45.M. J. Rice and S. Strassler, Solid State Commun. 13, 125 (1973)ADSCrossRefGoogle Scholar
- 45a.P. A. Lee, T. M. Rice and P. W. Anderson, Solid State Commun. 14, 703 (1974).ADSCrossRefGoogle Scholar
- 46.J. F. Scott, R. F. Leheny, J. P. Remeika and A. R. Sweedler, Phys. Rev. B2, 3883 (1970).ADSCrossRefGoogle Scholar

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