Abstract
Hole suppliers like Sr in doped La2CuO4 are mainly randomly distributed. Assuming that the holes are dislocated over a few lattice constants away from the Sr atom, the conducting areas form randomly distributed circles in the CuO2 layer planes. Conductivity and also superconductivity can occur only when these circles touch each other and form percolation clusters. Mobile holes are accompanied by diffusing d-electrons. Their spin direction is no longer localized on distinct places, and antiferromagnetism breaks down. The phase diagram of high-T c superconductors is discussed on the basis of a modified continuum percolation model for which the centers of each circle are located on lattice points. The inhomogeneities due to the random hole distributions lead to broad peaks instead of sharp singularities in the static and dynamic response functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
T. Schneider, J. of Superconductivity 17 41 (2004).
D. Poilblanc and T. M. Rice, Phys. Rev. B 39 9749 (1989).
J. Zaanen and O. Gunnarsson, Phys. Rev. B 40 7391 (1989).
A. Binconi, N. L. Saini, A. Lanzara, M. Missori, T. Rossetti, H. Oyanagi, H. Yamaguchi, K. Oka, and T. Ito, Phys. Rev. Lett. 76 3412 (1996).
K. M. Lang, V. Madhavan, J. E. Hoffman, E. W. Hudson, H. Eisaki, S. Uchida, and J. C. Davis, Nature 415 412 (2002).
J. C. Phillips, Phys. Rev. Lett. 88 216401 (2002).
J. C. Phillips, J. Supercond. In. Novel Magn 15 393 (2002).
D. Mihailovic, V. V. Kabanov, and K. A. Müller, Europhys. Lett. 57 254 (2002).
M. Mali, J. Roos, H. Keller, J. Karpinski, and K. Conder, Phys. Rev. B 65 184518 (2002).
Ch. P. Poole, T. Datta, and H. A. Farach, Copper Oxide Superconductors (Wiley, New York, 1988).
C. Domb, E. Stoll, and T. Schneider, Contemp. Phys. 21 577 (1980).
M. Rosso, J. Phys. A: Math. Gen. 22 L131 (1989).
S. B. Lee and S. Torquato, J. Chem. Phys. 89 6427 (1988).
E. P. Stoll, J. Mod. Phys. C 15 2 (in press 2004).
E. Hückel, Z. Physik 70 204 (1931); E. Hückel, Z. Physik 72 310 (1931); E. Hückel, Z. Physik 76 626 (1932).
R. Zallen, in Proceedings of the 13th IUPAP Conference on Statistical Physics, Vol. 1, D. Cabib, C. G. Kuper, and I. Riess, eds. (Israel Physical Society, 1978), p. 309.
C. Domb, T. Schneider, and E. Stoll, J. Phys. A: Math. Gen. 8 L90 (1975).
J. G. Bednorz and K. A. Müller, Z. Phys. B 64 189 (1986).
Erich Stoll, Max Kolb, and Eric Courtens, Phys. Rev. Lett. 68 2472 (1992).
P. W. Kasteleyn and C. M. Fortuin, J. Phys. Soc. Jpn Suppl. 26 11 (1969).
C. M. Fortuin and P. W. Kasteleyn, Physica 57 536 (1972).
M. F. Sykes, M. Glen, and D. S. Gaunt, J. Phys. A: Math. Gen. 7 L105 (1974).
Michael L. Williams and Humphrey J. Maris, Phys. Rev. B 31 4508 (1985).
K. Yakubo and T. Nakayama, Phys. Rev. B 40 517 (1989).
E. Courtens, R. Vacher, and E. Stoll, Physica D 38 41 (1989).
E. T. Gawlinsky and H. E. Stanley, J. Phys. A: Math. Gen. 14 L291 (1981).
J. Hoshen and R. Kopelman, Phys. Rev. B 28 5323 (1983).
E. Stoll, Comp. Phys. Comm. 109 1 (1998).
D. Stauffer, Introduction to Percolation Theory (Taylor and Francis, London, 1985).
E. Stoll and T. Schneider, J. Phys. A: Math. Gen. 9 L67 (1976).
Helen Au-Yang and Michael E. Fisher, Phys. Rev. B 11 3469 (1975).
G. Grinstein and A. Luther, Phys. Rev. B 13 1329 (1976).
Arthur E. Ferdinand and Michael E. Fisher, Phys. Rev. 185 832 (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stoll, E.P. Percolation, Fractal Behavior, and High-T c Superconductivity. Journal of Superconductivity 17, 79–84 (2004). https://doi.org/10.1023/B:JOSC.0000011845.48045.aa
Issue Date:
DOI: https://doi.org/10.1023/B:JOSC.0000011845.48045.aa