Magnetic Properties of Type-II Superconductors in the Two-Band Model

C. C. Sung

doi:10.1103/PhysRev.187.548

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Magnetic Properties of Type-II Superconductors in the Two-Band Model

C. C. Sung^*

Department of Physics, Ohio State University, Columbus, Ohio 43210

^*Research sponsored in part by the Air Force Office of Scientific Research, U. S. Air Force, under Grant No. AF-AFOSR-68-1487, through the Ohio State University Research Foundation.

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Phys. Rev. 187, 548 – Published 10 November, 1969

DOI: https://doi.org/10.1103/PhysRev.187.548

Abstract

It has been suggested previously by Wong and Sung that the present discrepancies between theory and experiments on the magnetic properties of some transition metals which are intrinsic type-II superconductors (e.g., Nb) may be caused by the overlapping-band effect of $s$ and $d$ bands. We present here the numerical results of this effect on the magnetic properties. It is shown that the overlapping-band effect in the pure limit can reduce the upper critical field $H_{c 2}$ about 30-60% at $T$ close to temperature $T_{c}$ , and thus enhance the over-all temperature dependence of $H_{c 2}$ . The amount of reduction decreases as the superconductors become dirtier. Reasonable parameters which characterize the overlapping-band effect are assumed. We also compute $κ_{2}$ , which defines the slope of $H_{c 2}$ when the external field is slightly less than $H_{c 2}$ . It is found that $κ_{2}$ becomes smaller in comparison with the present theory as $T \to T_{c}$ ; thus a stronger temperature dependence is also associated with $κ_{2}$ . The numerical value of this correction in $κ_{2}$ , however, is very sensitive to the parameters used.

References (25)

A. L. Fetter and P. C. Hohenberg, in Superconductivity, edited by R. D. Parks (M. Decker, Inc., New York, to be published), Chap. 14
K. Maki, Physics 1, 21 (1964) ibid.1, 27 (1964) C. Careli, M. Cyrot, and P. G. de Gennes, Solid State Commun. 4, 17 (1966) P. G. de Gennes, Phys. Kondensierten Materie 3, 79 (1964)
E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966)
G. Eilenberger, Phys. Rev. 153, 584 (1967)
D. K. Finnemore, T. F. Stromberg, and C. A. Swenson, Phys. Rev. 149, 231 (1966)
W. A. Fietz and W. W. Webb, Phys. Rev. 161, 423 (1967)
P. C. Hohenberg and N. R. Werthamer, Phys. Rev. 153, 493 (1967)
J. W. Garland, Phys. Rev. Letters 11, 111 (1963)
H. Suhl, B. J. Matthias, and L. R. Walker, Phys. Rev. Letters 3, 352 (1959)
L. Y. L. Shen, N. M. Senozen, and N. E. Phillips, Phys. Rev. Letters 14, 1025 (1965)
C. C. Sung and L. Y. L. Shen, Phys. Letters 19, 101 (1965)
V. K. Wong and C. C. Sung, Phys. Rev. Letters 19, 1236 (1967)
T. Soda and Y. Wada, Progr. Theoret. Phys. (Kyoto) 36, 1111 (1966)
D. R. Tilley, Proc. Phys. Soc. (London) 84, 573 (1964) I. Peschel, Solid State Commun. 4, 495 (1966)
V. A. Moskalenko, Zh. Eksperim. i Teor. Fiz. 51, 1162 (1966) [English transl.: Soviet Phys.—JETP 24, 780 (1967)] [12]
W. S. Chow, Phys. Rev. 176, 525 (1968)
Omitted endnote
A. A. Abrikosov, L. P. Gorkov and I. E. Dryaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963)
C. C. Sung and V. Wong, J. Phys. Chem. Solids 28, 1933 (1967)
H. Jones, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1956)
J. G. Daunt, in Progress in Low Temperature Physics, edited by C. J. Gorter (Wiley-Interscience, Inc., New York, 1955), Vol. I
Omitted endnote
Omitted endnote
T. Ohtsuka and N. Takano, J. Phys. Soc. Japan 23, 983 (1967) S. Williamson, Phys. Letters 28A, 665 (1969)
[4]

[c1] A. L. Fetter and P. C. Hohenberg, in Superconductivity, edited by R. D. Parks (M. Decker, Inc., New York, to be published), Chap. 14

[c2] K. Maki, Physics 1, 21 (1964) ibid.1, 27 (1964) C. Careli, M. Cyrot, and P. G. de Gennes, Solid State Commun. 4, 17 (1966) P. G. de Gennes, Phys. Kondensierten Materie 3, 79 (1964)

[c3] E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966)

[c4] G. Eilenberger, Phys. Rev. 153, 584 (1967)

[c5] D. K. Finnemore, T. F. Stromberg, and C. A. Swenson, Phys. Rev. 149, 231 (1966)

[c6] W. A. Fietz and W. W. Webb, Phys. Rev. 161, 423 (1967)

[c7] P. C. Hohenberg and N. R. Werthamer, Phys. Rev. 153, 493 (1967)

[c8] J. W. Garland, Phys. Rev. Letters 11, 111 (1963)

[c9] H. Suhl, B. J. Matthias, and L. R. Walker, Phys. Rev. Letters 3, 352 (1959)

[c10] L. Y. L. Shen, N. M. Senozen, and N. E. Phillips, Phys. Rev. Letters 14, 1025 (1965)

[c11] C. C. Sung and L. Y. L. Shen, Phys. Letters 19, 101 (1965)

[c12] V. K. Wong and C. C. Sung, Phys. Rev. Letters 19, 1236 (1967)

[c13] T. Soda and Y. Wada, Progr. Theoret. Phys. (Kyoto) 36, 1111 (1966)

[c14] D. R. Tilley, Proc. Phys. Soc. (London) 84, 573 (1964) I. Peschel, Solid State Commun. 4, 495 (1966)

[c15] V. A. Moskalenko, Zh. Eksperim. i Teor. Fiz. 51, 1162 (1966) [English transl.: Soviet Phys.—JETP 24, 780 (1967)] [12]

[c16] W. S. Chow, Phys. Rev. 176, 525 (1968)

[c17] Omitted endnote

[c18] A. A. Abrikosov, L. P. Gorkov and I. E. Dryaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963)

[c19] C. C. Sung and V. Wong, J. Phys. Chem. Solids 28, 1933 (1967)

[c20] H. Jones, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1956)

[c21] J. G. Daunt, in Progress in Low Temperature Physics, edited by C. J. Gorter (Wiley-Interscience, Inc., New York, 1955), Vol. I

[c22] Omitted endnote

[c23] Omitted endnote

[c24] T. Ohtsuka and N. Takano, J. Phys. Soc. Japan 23, 983 (1967) S. Williamson, Phys. Letters 28A, 665 (1969)

[c25] [4]

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Magnetic Properties of Type-II Superconductors in the Two-Band Model

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