Theory of finite-size effects and vortex penetration in small Josephson junctions

Abstract

We present a study of finite-size effects in a small Josephson junction. Explicit expressions for the total magnetic field have been found for the case of the Meissner state and for that of an ordered array of Abrikosov vortices penetrating the electrodes. We have determined how the behavior of the critical current Ic as a function of the strength of an external magnetic field depends on the ratio L/λx of the width of the junction to the appropriate London penetration length. For small L/λx in particular, significant deviations from the familiar Fraunhofer pattern are found in a number of situations. We find that, in general, for the same field strength, because of an interesting cancellation property of the Josephson phase gradient, vortex penetration tends to increase the critical current. Moreover, for suitable vortex configurations Ic is found to be determined by the magnetization and to actually increase with the field. The relevance of our results for junctions made out of high-temperature superconductors is discussed.

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