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The effect of cracks on the superconducting transport current in thin films: The analogy with two-dimensional elasticity and plasticity

Published online by Cambridge University Press:  31 January 2011

David R. Clarke  and
Marc DeGraef
David R. Clarke
Affiliation:
Materials Department, University of California, Santa Barbara, California 93106
Marc DeGraef
Affiliation:
Materials Department, University of California, Santa Barbara, California 93106
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Abstract

Simulations of arrays of resistively shunted Josephson junctions containing a crack of uncoupled junctions indicate that the crack can distort the supercurrent flow and provide a nucleation site at the crack tip for the formation of superconducting vortices at applied currents below the critical current of the homogeneous material. An analogy is established between the supercurrent distribution in two dimensions and the stress field distribution around the crack for antiplane mechanical loading. The analogy is used to show that the supercurrent distribution can be described analytically in terms of a Westergaard function used in elasticity theory. In addition, using a correspondence between the forces acting on a vortex and a crystal dislocation, models for screw dislocation emission from a crack tip are transposed to describe vortex emission from a crack tip. These lead to predictions for the pinning force required to prevent dissipation by vortex emission from the crack tip, as well as for the size of a vortex zone ahead of the crack for different values of the ratio of the applied current to the pinning force.

Type
Articles
Information
Journal of Materials Research , Volume 8 , Issue 7 , July 1993 , pp. 1515 - 1532
Copyright
Copyright © Materials Research Society 1993

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References

REFERENCES

1Olsson, E.Gupta, A., Thouless, M. D. and Clarke, D. R.Appl. Phys. Lett. 58, 1682 (1991).CrossRefGoogle Scholar
2Hellman, E. S.Hartford, E. H. and Gyorgy, E.M., Appl. Phys. Lett. 58, 1335 (1991).CrossRefGoogle Scholar
3Shaw, T. M.Shinde, S. L.Dimos, D., Cook, R. F.Duncombe, P. R. and Kroll, C.J. Mater. Res. 4, 248 (1989).CrossRefGoogle Scholar
4Clarke, D. R.Shaw, T. M. and Dimos, D.J. Am. Ceram. Soc. 72, 1103 (1989).Google Scholar
5Evans, A. G.Act a Metall. 26, 1845 (1978).Google Scholar
6Clarke, D. R.Act a Metall. 28, 913 (1980).Google Scholar
7Kim, S.G. and Duxbury, P.M.J. Appl. Phys. 70, 3164 (1991).Google Scholar
8Xia, W. and Leath, P. L.Phys. Rev. Lett. 63, 1428 (1989).CrossRefGoogle Scholar
9Haasen, P.Contemporar y Physics 18, 373 (1977).Google Scholar
10Hilzinger, H. R.Philos. Mag. 36, 225 (1977).CrossRefGoogle Scholar
11Clem, J.R.Physica C 153–155, 56 (1988).Google Scholar
12Dimos, D., Mannhart, J. and Chaudhari, P.Phys. Rev. B 41, 4038 (1990).CrossRefGoogle Scholar
13Nichols, C. S. and Clarke, D. R.Act a Metall. 39, 995 (1991).Google Scholar
14McCumber, D.E.J. Appl. Phys. 39, 3113 (1968).Google Scholar
15Stewart, W. C.Appl.Phys. Lett. 12, 277 (1968).CrossRefGoogle Scholar
16Tinkham, M.Introduction to Superconductivity (R. E. Krieger New York, 1980).Google Scholar
17Duzer, T. Van and Turner, C. W.Principles of Superconductive Devices and Circuits (Elsevier, New York, 1981).Google Scholar
18Westergaard, H. M.J. Appl. Mech. 6, 49–53 (1939).CrossRefGoogle Scholar
19Tada, H.Paris, P. C. and Irwin, G. R.The Stress Analysis of Cracks Handbook (Del Research, 1978).Google Scholar
20Sih, G. C.Handbook of Stress Intensity Factors (Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, PA).Google Scholar
21Rice, J. R., J. Appl. Mech. 35, 379 (1968).CrossRefGoogle Scholar
22Rice, J.R. and Thomson, R.M.Philos. Mag. 29, 73 (1974).CrossRefGoogle Scholar
23Gennes, P. G. de, Superconductivity of Metals and Alloys (W. A. Benjamin, New York, 1966).Google Scholar
24Hirth, J. P. and Lothe, J.Theory of Dislocations (McGraw-Hill, New York, 1968).Google Scholar
25Peach, M. O. and Koehler, J. S.Phys. Rev. 80, 436 (1950).CrossRefGoogle Scholar
26Thomson, R. M.Solid State Phys. 39, 1 (1986).Google Scholar
27Chiao, Y.H. and Clarke, D.R.Act a Metall. 37, 203 (1989).Google Scholar
28Tinkham, M. and Lobb, C.J.Solid State Phys. 42, 91 (1989).Google Scholar
29Bilby, B. A.Cottrell, A. H. and Swinden, K. H.Proc. R. Soc. A 272, 304 (1963).Google Scholar
30Bilby, B. A. and Eshelby, J. D. in Fracture, edited by Leibowitz, H., 1, 99.Google Scholar
31Livingston, J.D.Phys. Status Solidi 44, 295 (1977).CrossRefGoogle Scholar
32Lee, P. J. and Larbalestier, D. C.Acta Metall. 35, 2523 (1987).Google Scholar
33Campbell, A.M. and Evetts, J.E.Adv. Phys. 21, 199 (1972).CrossRefGoogle Scholar
34Labusch, R.CrystalLattice Defects 1, 1 (1969).Google Scholar
35Kramer, E.J.J. Appl. Phys. 41, 621 (1971).Google Scholar
36Kramer, E.J.J. Appl. Phys. 44, 1360 (1973).CrossRefGoogle Scholar
37Trauble, H. and Essmann, U.J. Appl. Phys. 39,4052 (1968).CrossRefGoogle Scholar
38Essmann, U. and Trauble, H.Phys. Status Solidi 32, 337 (1969).CrossRefGoogle Scholar
39Herring, C.Phys. Lett. A 47, 105 (1974).Google Scholar
40Dolan, G. J.Chandrashekhar, G. V.Dinger, T. R.Feild, C. and Holtzberg, F.Phys. Rev. Lett. 62, 827 (1989).Google Scholar
41Sarma, N.V.Phys. Lett. A 25, 315 (1967).CrossRefGoogle Scholar
42Krageloh, U.Phys. Status Solidi 42, 559 (1970).CrossRefGoogle Scholar
43Beasley, M. R.Labusch, R. and Webb, W. W.Phys. Rev. 181, 682 (1969).CrossRefGoogle Scholar
44Rice, J.R.J. Mech. and Phys. Solids 40, 239 (1992).CrossRefGoogle Scholar