Penetration of magnetic field into a long periodically modulated Josephson contact

Abstract

A new approach to magnetic field profiling inside a Josephson contact is suggested. Its essence consists in analyzing continuous variation of a current configuration leading to a decrease in the Gibbs potential. With this approach, one can find a configuration into which the Meissner state turns when an external field slightly exceeds the upper boundary of the Meissner regime and trace the evolution of this configuration with increasing field. Calculations show that there exists critical value I _c of the pinning parameter in the range 0.95–1.00. This critical value separates two possible conditions of magnetic field penetration into the contact. At I > I _c, a near-boundary current configuration completely compensating for the external field inside the contact arises irrespective of the external field strength. At I < I _c, such a situation is observed only until the external field strength exceeds certain value H _max. Higher fields penetrate into the contact indefinitely deep. In nearboundary configurations, the magnetic field drops with increasing depth almost linearly. Its slope k has rational values, which remain constant within finite intervals of I. As I goes beyond a given interval, k rises stepwise and takes on another rational value. When an external magnetic field is switched on adiabatically, configurations with a maximal growth rate of the magnetic field are observed.