Abstract
Connecting perfect one-dimensional leads to sites i and j on the quantum percolation (QP) model, we calculate the transmission coefficient T ij (E) at an energy E near the band center and the averages of \(\sum\nolimits_{ij} {{T_{ij}}} ,\,\sum\nolimits_{ij} r _{ij}^2{T_{ij}}\,and\,\sum\nolimits_{ij} r _{ij}^4{T_{ij}}\,\) to 10th order in the concentration p. All three series diverge at a finite threshold p q , with exponents γ, γ+2ν and γ+4ν We find ν = 0.38 ± 0.07in 3 dimensions, differing from “usual” Anderson localization and violating the bound ν ≥ 2/d of Chayes et al. Thus, QP belongs to a new universality class.
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References
P. W. Anderson, Phys. Rev. 109, 1492 (1958).
P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
E. Abrahams, P. W. Anderson, D. C. Liciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
Y. Meir, A. Aharony, and A. B. Harris, Europhys. Lett. 10, 275 (1989), where a discussion of relevant earlier references is given.
C. M. Soukoulis, Q. Li and G. S. Grest, Phys. Rev. B 44, 4685 (1991).
J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Phys. Rev. Lett. 57, 2999 (1986).
S. Kirkpatrick and T. P. Eggarter, Phys. Rev. B 6, 3598 (1972).
Y. Shapir, A. Aharony, and A. B. Harris, Phys. Rev. Lett. 49, 486 (1982).
J. Adler et al., J. Stat. Phys. 58, 511 (1990).
A. B. Harris, Phys. Rev. Lett. 49, 296 (1982).
C. C. Wan, A. B. Harris, and J. Adler, J. Appl. Phys. 69, 5191 (1991).
I. Chang, Z. Lev, A. B. Harris, J. Adler and A. Aharony, Phys. Rev. Lett. 74, 2094 (1995).
J. L. Gammel, in Pade Approximanis and Their Applications, ed. B. R. Graves-Morris (Academic Press, New York, N. Y., 1973 ).
J. Adler, I. Chang, and S. Shapira, Int. J. Mod. Phys. C 4, 1007 (1993).
J. Adler, Y. Meir, A. Aharony, A. B. Harris, and L. Klein, J. Stat. Phys. 58, 511 (1990); J. Adler, M. Moshe, and V. Privman, Phys. Rev. B 26, 3958 (1982).
J. Adler and D. Stauffer, Physica A 181, 396 (1992).
M. Gofman, J. Adler, A. Aharony, A. B. Harris, and M. Schwartz, Phys. Rev. Lett. 71, 1569 (1993); (E) 2841.
T. Odagaki and K. C. Chang, Phys. Rev. B 30, 1612 (1984); K. C. Chang and T. Odagaki, J. Phys. A 20, L1027 (1987).
C. M. Soukoulis and G. S. Grest, Phys. Rev. B 45, 7724 (1992).
D. L. Hunter and G. A. Baker, Phys. Rev. B 7, 3346 (1973).
Y. Meir, J. Phys. A 20, L349 (1987).
Details will be published elsewhere.
e. g., E. Hofstetter and M. Schreiber, Europhys. Lett. 21, 933 (1993).
D. S. Fisher. Phys. Rev. Lett. 69, 534 (1992).
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Chang, I., Lev, Z., Harris, A.B., Adler, J., Aharony, A. (1995). Localization Transition in Quantum Percolation. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics VIII. Springer Proceedings in Physics, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79991-4_15
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DOI: https://doi.org/10.1007/978-3-642-79991-4_15
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