Abstract
An iterative procedure has been developed to solve Eilenberger's version of the Gor'kov equations numerically. The method has been used to compute the structure of flux lines and the lower critical field for clean superconductors as a function of temperature. Some information on the vortex lattice has also been obtained by means of a circular cell approximation. We find a pronounced reduction in the size of the coreregion (measured, e.g., in units of the temperature-dependent coherence length) with decreasing temperature; this results in considerably steeper slopes of the order parameter and the current density at the vortex center. There are indications that, among other peculiar effects, these slopes diverge forT → 0. The field at the center of the isolated vortex apparently increases with decreasing temperature down toT=0. The results are compared with experiments and with similar calculations for the dirty limit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Abrikosov,Soviet Phys.—JETP 5, 1174 (1957); L. P. Gor'kov,Soviet Phys.—JETP 9, 1364 (1959);Soviet Phys.—JETP 10, 998 (1960).
L. Tewordt,Z. Phys. 180, 385 (1964);Z. Phys. 184, 319 (1965);Phys. Rev. 137A, 1745 (1965). L. Neumann and L. Tewordt,Z. Phys. 191, 73 (1966).
L. Neumann and L. Tewordt,Z. Phys. 189, 55 (1966).
E. Helfand and N. R. Werthamer,Phys. Rev. 147, 288 (1966).
G. Eilenberger,Phys. Rev. 153, 584 (1967).
G. Eilenberger,Z. Phys. 214, 195 (1968).
G. Eilenberger and H. Büttner,Z. Phys. 224, 335 (1969).
M. C. Leung and A. E. Jacobs,J. Low Temp. Phys. 11, 395 (1973).
L. Kramer,Z. Phys. 258, 367 (1973); M. C. Leung,J. Low Temp. Phys. 12, 215 (1973).
K. Usadel,Phys. Rev. Letters 25, 507 (1970).
L. Kramer, W. Pesch, and R. J. Watts-Tobin, to be published inJ. Low Temp. Phys. 14, 29 (1974).
L. Kramer and W. Pesch, inLow Temperature Physics LT-13 (13th Int. Conf. Low Temp. Phys., Boulder, Colorado, 1972) (Plenum, New York, 1973), Vol. 3, p. 49.
L. Kramer and W. Pesch,Solid State Commun. 12, 549 (1973).
J. Bardeen, R. Kümmel, A. E. Jacobs, and L. Tewordt,Phys. Rev. 187, 556 (1969).
J. M. Ortega and W. G. Reinboldt,Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).
J. M. Delrieu,J. Low Temp. Phys. 6, 197 (1971).
E. H. Brandt,Phys. Lett. 43A, 539 (1973).
A. Kung,Phys. Rev. Lett. 25, 1006 (1970).
G. Lippmann, J. Schelten, H. Ullmaier, private communication.
J. Schelten, H. Ullmaier, and G. Lippmann,Z. Phys. 253, 219 (1972); H. Ullmaier, J. Schelten, W. Schmatz, and G. Lippmann, inLow Temperature Physics LT-13 (13th Int. Conf. Low Temp. Phys., Boulder, Colorado, 1972) (Plenum, New York, 1973).
H. W. Weber, J. Schelten, and G. Lippmann,Phys. Stat. Sol. (b) 57, 515 (1973).
U. Kumpf,Phys. Stat. Sol. (b) 44, 829 (1971).
J. Auer and H. Ullmaier,Phys. Rev. B 7, 136 (1973).
R. Radebaugh and P. H. Keesom,Phys. Rev. 149, 209 (1966);Phys. Rev. 149, 217 (1966).
D. K. Finnemore, T. F. Stromberg, and T. A. Swenson,Phys. Rev. 149, 231 (1966).
H. Ullmaier, R. H. Kernohan, E. Cruceanu, and E. Hering,J. Low Temp. Phys. 5, 71 (1971).
J. Wollan and D. K. Finnemore, unpublished.
K. W. Haas and D. K. Finnemore, unpublished.
J. Ferreira da Silva, E. A. Burgemeister, and Z. Dokoupil,Physica 41, 409 (1969).
U. Brandt, W. Pesch, and L. Tewordt,Z. Phys. 201, 209 (1967).
R. J. Watts-Tobin and G. M. Waterworth, inLow Temperature Physics LT-13 (13th Int. Conf. Low Temp. Phys., Boulder, Colorado, 1972) (Plenum, New York, 1973);Z Phys. 261, 249 (1973).
K. Noto, Y. Muto, and T. Fukuroi,J. Phys. Soc. Japan 21, 2122 (1966).
Author information
Authors and Affiliations
Additional information
On leave from Abteilung für Theoretische Festkörperphysik am Institut für Angewandte Physik der Universität Hamburg, Germany.
Rights and permissions
About this article
Cite this article
Pesch, W., Kramer, L. Local structure and thermodynamic properties of clean type II superconductors nearH c1 at arbitrary temperature. J Low Temp Phys 15, 367–386 (1974). https://doi.org/10.1007/BF00661192
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00661192