Transmission coefficients of superconducting particles

Objectives. There is no general theory of superconductivity capable of fully describing this phenomenon, which imposes its own difficulties in the search for new superconducting materials, as well as in the study of their properties. In particular, the electrodynamics of a superconducting system is unexplored. With the aim of a possible further description of the electrodynamics of superconductors, the temperature dependences of the energy parameters of a Cooper pair in the potential field of Abrikosov vortex were analyzed. Methods. The basis for the obtained results of the work was the consideration of the transmission coefficient for a superconducting particle in the approximation of the Wentzel– Kramers–Brillouin method, as well as the relationship between the critical temperature and the London penetration depth and the coherence length based on the model of plasmon destruction of the superconducting state. Results. The dependences of the lifetime of a particle in a potential well, penetration depth, frequency of impacts of a particle against a potential barrier, blurring of the energy level, transmission coefficient, and potential and kinetic energy of a particle on temperature were obtained. The characteristic values of these parameters were obtained at absolute zero for various cuprate, organic, and other superconducting materials. The dependences of the critical electric potential on temperature, as well as the London penetration depth, coherence length, and electric potential on the transmission coefficient at different temperatures were obtained. The form of the dependences qualitatively corresponds to the experimental data. Conclusions. The results obtained can be used to construct a general theory of superconductivity, describe the electrodynamics of a superconducting state, and develop new superconductors with higher critical currents.