HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 40 (1968) > Number 2
| Next Article >

Prog. Theor. Phys. Vol. 40 No. 2 (1968) pp. 193-200

[ Full Text PDF : FREE ACCESS (422K) ]

Critical Fluctuation of the Order Parameter in a Superconductor. I

Kazumi Maki

Department of Physics, Tohoku University, Sendai

(Received March 30, 1968)

Abstract:

The fluctuation of the order parameter in a superconductor in the temperature slightly above the transition temperature is studied in the framework of the current microscopic theory. It is convenient to divide the temperature region where the fluctuation of the order parameter becomes important into two regions; the classical and the critical region. In the classical region the spatial correlation of the fluctuation is of the Ornstein-Zernike type, while in the critical region it depends on the relative distance like r-3/2. We show that the electrical resistivity, the nuclear spin lattice relaxation time and the ultrasonic attenuation coefficient decrease like 1-a|η|-1/2 and 1-a'|η|-1/3 in the classical and in the critical region respectively, where η=(T/Tc)-1 and a and a' are constants of the order (Tc/µ)1/2(lp0)-3/2 and (Tc/µ)1/3(lp0)-1 respectively. Here µ is the chemical potential, l is the electronic mean free path and p0 is the fermi momentum.
It is also shown that the thermal conducivity has no singular term at the transition temperature.


URL : http://ptp.ipap.jp/link?PTP/40/193/
DOI : 10.1143/PTP.40.193

[ Full Text PDF : FREE ACCESS (422K) ] Citation:

References:

  1. C. Caroli and K. Maki, Phys. Rev. 159 (1967), 306[APS]; ibid. 159 (1967), 316[APS].
  2. D. J. Thouless, Ann. of Phys. 10 (1960), 553[CrossRef].
  3. É. G. Batyev, A. Z. Patashinskii and V. L. Pokrovskii, Zh. Eksp. Teor. Fiz. 46 (1964), 2093 [Sov. Phys. -JETP 19 (1964) 1412].
  4. G. Eilenberger, Phys. Rev. 164 (1967), 628[APS].
  5. R. A. Ferrell and H. Schmidt, Phys. Lett. A 25 (1967), 544[CrossRef].
  6. R. E. Glover, Phys. Lett. A 25 (1967), 542[CrossRef].
  7. L. P. Gor'kov, Zh. Eksp. Teor. Fiz. 36 (1959), 1918; ibid. 37 (1959), 1407 [Sov. Phys. -JETP 9 (1959), 1364; ibid. 10 (1960), 998].
  8. P. W. Anderson, Proceedings of the Conference on Critical Phenomena, Washington, 1965, eds. M. S. Green and J. V. Sengers, p. 102.
  9. K. Maki, Phys. Rev. 141 (1966), 331[APS].
    K. Maki, Prog. Theor. Phys. 39 (1968), 897[PTP].
  10. See for the corresponding expressions in dirty type II superconductors, K. Maki, “gapless superconductivity” in a treatise on Superconductivity, edited by R. D. Parks (to be published by Marcel Dekker, Inc., New York).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 3744-3745 :
    Superconducting Fluctuation Effects on N-I-N Tunneling Current
    Kenji Takanaka
  2. Journal of the Physical Society of Japan 59 (1990) pp. 2205-2210 :
    Paraconductivity and Temperature-Dependent Pair-Breaking Parameter in Superconducting Niobium Thin Films
    Natsuki Mori, Takayuki Kobayashi, Teruhisa Shimizu and Hajime Ozaki
  3. Journal of the Physical Society of Japan 68 (1999) pp. 2999-3015 :
    Theory of Pseudogap Phenomena in High-T c Cuprates Based on the Strong Coupling Superconductivity
    Youichi Yanase and Kosaku Yamada
  4. Journal of the Physical Society of Japan 69 (2000) pp. 2209-2220 :
    Effect of Magnetic field on the Pseudogap Phenomena in High-T c Cuprates
    Youichi Yanase and Kosaku Yamada
  5. Journal of the Physical Society of Japan 69 (2000) pp. 3664-3677 :
    Theory on Superconducting Transition from Pseudogap State
    Youichi Yanase, Takanobu Jujo and Kosaku Yamada
  6. Journal of the Physical Society of Japan 70 (2001) pp. 498-504 :
    Fluctuation Paraconductivity in Superconducting Multilead Structures above the Transition Temperature
    Yositake Takane
  7. Journal of the Physical Society of Japan 70 (2001) pp. 1659-1680 :
    Pseudogap Phenomena and Superconducting Fluctuations in Hubbard Model for High-Tc Cuprates
    Youichi Yanase and Kosaku Yamada
  8. Journal of the Physical Society of Japan 71 (2002) pp. 278-292 :
    Theory of Electric Transport in the Pseudogap State of High-Tc Cuprates
    Youichi Yanase
  9. Progress of Theoretical Physics Vol. 41 No. 2 (1969) pp. 296-306 :
    Dynamic Critical Fluctuation of Superconductivity Order Parameter above the Transition Point
    Toshio Tsuzuki
  10. Progress of Theoretical Physics Vol. 43 No. 2 (1970) pp. 286-302 :
    Nonlinear Response above the Superconducting Transition Point. III
    Toshio Tsuzuki
  11. Progress of Theoretical Physics Vol. 43 No. 6 (1970) pp. 1445-1457 :
    Effect of Fluctuations in the Superconducting Order Parameter on the Electronic States
    Hajime Takayama
  12. Progress of Theoretical Physics Vol. 44 No. 6 (1970) pp. 1450-1471 :
    Linear Response Theory in the Vortex State of Dirty Type-II Superconductors
    Hajime Takayama and Hiromichi Ebisawa
  13. Progress of Theoretical Physics Vol. 45 No. 2 (1971) pp. 365-369 :
    Microscopic Derivation of the Langevin Equation for the Order Parameter in Superconductors
    Arisato Kawabata
  14. Progress of Theoretical Physics Vol. 45 No. 3 (1971) pp. 693-703 :
    Microscopic Theory of the Nonlinear Excess Current of Superconducting Thin Films near Tc
    Kunihiko Yamaji
  15. Progress of Theoretical Physics Vol. 45 No. 4 (1971) pp. 1016-1020 :
    Nonlinear Field Dependence of Electric Conductivity above the Superconducting Transition
    Kazumi Maki
  16. Progress of Theoretical Physics Vol. 46 No. 1 (1971) pp. 1-14 :
    Superconducting Fluctuation Effects on the S-I-N Junction Current
    Hajime Takayama
  17. Progress of Theoretical Physics Vol. 46 No. 1 (1971) pp. 42-62 :
    Higher Order Effects Due to Superconducting Fluctuation on Electrical Conductivity
    Hajime Takayama and Kazumi Maki
  18. Progress of Theoretical Physics Vol. 46 No. 6 (1971) pp. 1651-1665 :
    Thermodynamic Fluctuation of the Order Parameter in the Vortex State of Type II Superconductors
    Kazumi Maki and Hajime Takayama
  19. Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 1-18 :
    On the Nonperturbational Calculation of Critical Anomalies of Superconductors in External Fields
    Masao Koyanagi
  20. Progress of Theoretical Physics Vol. 48 No. 2 (1972) pp. 382-406 :
    Functional Integral Method on Superconducting Critical Phenomena. I
    Hajime Takayama
  21. Progress of Theoretical Physics Vol. 48 No. 3 (1972) pp. 758-765 :
    Functional Integral Method on Superconducting Critical Phenomena. II
    Hajime Takayama
  22. Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 740-752 :
    Effect of Electric Fields on the Excess Electric Current of the Maki Process above the Superconducting Transition Point
    Masao Koyanagi
  23. Progress of Theoretical Physics Vol. 54 No. 3 (1975) pp. 624-641 :
    Fluctuation Conductivity and Vortex Flow Resistivity of a Dirty Strong-Coupling Superconductor
    Syozo Imai
  24. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 15-32 :
    Electrical Conductivity above the Superconducting Transition Temperature in Quasi-One-Dimensional Conductors
    Kiyomi Okamoto and Mitsunobu Wakata
  25. Progress of Theoretical Physics Vol. 114 No. 1 (2005) pp. 117-155 :
    Pre-Critical Phenomena of Two-Flavor Color Superconductivity in Heated Quark Matter
    Masakiyo Kitazawa, Tomoi Koide, Teiji Kunihiro and Yukio Nemoto
  26. Progress of Theoretical Physics Supplement No.84 (1985) pp. 47-68 :
    Interaction Effects in Anderson Localization
    Hidetoshi Fukuyama

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.