The Cooper Pair Behavior in the Abrikosov Vortex Potential Field

At present, there is no complete theory of superconductivity, which entails the need to solve a number of important research tasks and problems. In particular, studying the dynamic behavior of a superconducting system is of key importance for understanding the processes occurring in superconductors and for their practical application. The behavior of a Cooper pair in the potential field of an Abrikosov vortex is considered, and the process physics is qualitatively described. The system characteristic length and energy are estimated on the basis of the Heisenberg uncertainty and the quasi classical method. The theoretical and experimental coherence lengths for cuprate superconductors are compared with each other, and good agreement of the estimates is achieved for many cuprate superconductors. The obtained estimate of the coherence length indicates the physics of the process, according to which the Cooper pairs in the vortex superconducting region can be considered in some approximation as a gas of particles. The obtained forms of the coherence length estimates resemble the expression for the molecule effective diameter if the London length is regarded as the molecule mean free path, and the coherence length as the effective diameter. The Schrodinger equation for the Cooper pair is analyzed, and the dependences of the wave function of a particle in the vortex superconducting and non-superconducting regions are derived. Solutions are obtained for two cases in which the particle total energy is more or less than its potential energy. In the second case, it can be seen that the wave function at the vortex center does not equal zero, but has a finite value, which points to possible quantization of the Cooper pair energy in the Abrikosov vortex inner region. The obtained results can be used for developing a complete theory of superconductivity and can serve as the starting point for developing a theory of superconducting system dynamics, which will entail, in particular, a description of the current-voltage characteristics of superconductors of the second kind.