Bulk Upper Critical Field of Clean Type-II Superconductors: V and Nb

S. J. Williamson

doi:10.1103/PhysRevB.2.3545

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Bulk Upper Critical Field of Clean Type-II Superconductors: V and Nb

S. J. Williamson^*

Science Center, North American Rockwell Corporation, Thousand Oaks, California 91360

^*Present address: Department of Physics, University of California, Santa Barbara, Calif. 93106.

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Phys. Rev. B 2, 3545 – Published 1 November, 1970

DOI: https://doi.org/10.1103/PhysRevB.2.3545

Abstract

The bulk upper critical field $H_{c 2}$ of single crystals of Nb and V has been measured for various crystallographic orientations within the temperature range between the respective critical temperature and $T \approx 0. 06$ °K. The normalized critical field averaged over all crystallographic directions $〈 h (t) 〉 = \frac{〈 H_{c 2} (t) 〉}{{(- \frac{d H_{c 2}}{dt})}_{t = 1}}$ , where $t = \frac{T}{T_{c}}$ , and the relative anisotropy of $H_{c 2}$ for the two metals are found to be similar. The measurements support predictions of the Hohenberg-Werthamer calculation that attributes the observed anisotropy of $H_{c 2}$ to the effects of an anisotropic Fermi surface. Some differences in the behavior of $H_{c 2} (t)$ for the present samples can be understood qualitatively to arise from the effects of a shorter electron-collision time $τ$ for the less pure V specimen. At very low temperatures, $H_{c 2} (0) - H_{c 2} (t)$ for V does not follow a $t^{2} \ln (t)$ temperature dependence, previously observed for Nb, but can be characterized by an empirical formula $t^{2} \ln (t + α)$ in which the constant $α$ is conjectured to be inversely proportional to $τ$ .

References (45)

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[c1] T. Sugawara and H. Egnchi, in Proceedings of the Tenth International Conference on Low Temperature Physics, Moscow, 1966, edited by M. P. Malkov (Proizvodstenno-Izdatel' skii Kombinet, VINITI, Moscow, 1967), Vol. IIA, p. 288

[c2] D. R. Tilley, G. J. van Gurp, and C. W. Berghout, Phys. Letters 12, 305 (1964)

[c3] A. L. Fetter and P. C. Hohenberg, in Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969), Vol. 2, p. 817

[c4] W. A. Reed, E. Fawcett, P. P. M. Meincke, P. C. Hohenberg, and N. R. Werthamer, in Proceedings of the Tenth International Conference on Low Temperature Physics, Moscow, 1966, edited by M. P. Malkov (Proizvodstenno-Izdatel' skii Kombinet, VINITI, Moscow, 1967), Vol. IIA, p. 368

[c5] P. C. Hohenberg and N. R. Werthamer, Phys. Rev. 153, 493 (1967)

[c6] T. McConville and B. Serin, Phys. Rev. 140, A1169 (1965)

[c7] L. C. Skinner, II, R. M. Rose, and J. Wulff, J. Appl. Phys. 37, 2191 (1966)

[c8] D. K. Finnemore, T. F. Stromberg, and C. A. Swenson, Phys. Rev. 149, 231 (1966)

[c9] T. Ohtsuka and N. Takano, J. Phys. Soc. Japan 23, 983 (1967)

[c10] W. A. Fietz and W. W. Webb, Phys. Rev. 161, 423 (1967)

[c11] R. A. French, Cryogenics 8, 301 (1968) R. A. French and J. Lowell, Phys. Rev. 173, 504 (1968)

[c12] A. Ikushima, T. Mizusaki, and T. Odaka, Phys. Letters 26A, 582 (1968)

[c13] R. Radebaugh and P. H. Keesom, Phys. Rev. 149, 217 (1966)

[c14] E. Helfand and N. R. Werthamer, Phys. Rev. Letters 13, 686 (1964) Phys. Rev. 147, 288 (1966)

[c15] L. F. Mattheiss, Phys. Rev. B 1, 373 (1970)

[c16] S. J. Williamson and L. Valby, Phys. Rev. Letters 24, 1061 (1970)

[c17] V. K. Wong and C. C. Sung, Phys. Rev. Letters 19, 1236 (1967) C. C. Sung, Phys. Rev. 187, 548 (1969) V. Radhakrishnan, Nuovo Cimento 48, 1671 (1967)

[c18] K. S. Nelson, J. L. Stanford, and F. A. Schmidt, Phys. Letters 28A, 402 (1968)

[c19] I. Williams and A. M. Court, Solid State Commun. 7, 169 (1969)

[c20] S. J. Williamson, Rev. Sci. Instr. 40, 1632 (1969)

[c21] J. C. Wheatley, O. E. Vilches, and W. R. Abel, Physics 4, 1 (1968)

[c22] Omitted endnote

[c23] J. P. Franck and D. L. Martin, Can. J. Phys. 39, 1320 (1961)

[c24] L. Y. L. Shen, N. M. Senozan, and N. E. Phillips, Phys. Rev. Letters 14, 1025 (1965)

[c25] F. C. Von der Lage and H. A. Bethe, Phys. Rev. 71, 612 (1947)

[c26] S. L. Altmann and A. P. Cracknell, Rev. Mod. Phys. 37, 19 (1965)

[c27] S. L. Altmann and C. J. Bradley, Phil. Trans. Roy. Soc. London A255, 199 (1963)

[c28] F. M. Mueller and M. G. Priestley, Phys. Rev. 148, 638 (1966)

[c29] D. E. Farrell, B. S. Chandrasekhar, and S. Huang, Phys. Rev. 176, 562 (1968)

[c30] M. L. A. MacVicar and R. M. Rose, J. Appl. Phys. 39, 1721 (1968)

[c31] W. L. McMillan, Phys. Rev. 167, 331 (1968)

[c32] N. R. Werthamer and W. L. McMillan, Phys. Rev. 158, 415 (1967)

[c33] G. Eilenberger and V. Ambegaokar, Phys. Rev. 158, 332 (1967)

[c34] W. L. McMillan and P. C. Hohenberg (private communication)

[c35] K. Takanaka and T. Nagashima, Progr. Theoret. Phys. (Kyoto) 43, 18 (1970)

[c36] S. J. Williamson, Phys. Letters 23, 629 (1966)

[c37] L. P. Gor'kov, Zh. Eksperim. i Teor. Fiz. 37, 833 (1959) [Soviet Phys. JETP 10, 593 (1960)]

[c38] U. Brandt, Phys. Letters 29A, 568 (1969)

[c39] K. Maki and T. Tsuzuki, Phys. Rev. 139, A868 (1965)

[c40] P. Carsey, R. Kagiwada, M. Levy, and K. Maki (unpublished)

[c41] R. R. Hake (private communication)

[c42] S. J. Williamson, Phys. Letters 28A, 665 (1969)

[c43] J. R. Carlson and C. B. Satterthwaite, Phys. Rev. Letters 24, 461 (1970)

[c44] J. W. Hafstrom, R. M. Rose, and M. L. A. MacVicar, Phys. Letters 30A, 379 (1969)

[c45] K. Takanaka, Twelfth International Conference on Low Temperature Physics, Kyoto, September, 1970 (unpublished)

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Bulk Upper Critical Field of Clean Type-II Superconductors: V and Nb

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