Lower critical field of a long Josephson S-I-S tunnel junction with quantum jumpers in \(I\) layer
The paper represents the formulas for the lower critical field, at which the vortex-free (Meissner) state of a long junction becomes unstable, and mesoscopic structural fluctuations of the lower critical field. These formulas are obtained in the energy range of tunnel resonances of a long superconductor-insulator-superconductor (S-I-S) tunnel junction with weak (at the low impurity concentrations) structural disorder in the \(I\) layer. The S-I-S sandwich is considered in a magnetic field oriented parallel to the junction plane at \(T = 0\). Identical electron-attracting impurities are randomly embedded in the insulator. First, the lower critical field is written for a given random impurity configuration through the free energy per solitary fluxon. The phase difference of the superconducting order parameters in S pieces satisfies the 1D steady-state sine-Gordon equation, in which the random coefficient is expressed in terms of a random local tunnel transparency of the \(I\) layer. Then, this coefficient is written via a small parameter. After an averaging over the ensemble of impurity configurations and passing to the dimensionless coordinate, the authors obtain an ordinary differential equation for the phase difference. The free energy is present through the first-order terms in the small parameter as a function of the unperturbed solution of the differential equation. This solution corresponds to the mean-field approximation for a solitary fluxon in the energy range of tunnel resonances of the \(I\) layer. Finally, the lower critical field and its relative function are expressed in terms of the average tunnel conductivity and the correlation function of its spatial fluctuations in the energy range of tunnel resonances, taking into account their representations in the form of sums over quantum resonance-percolation trajectories.
scientific article; zbMATH DE number 5656598