ANALYTICAL SOLUTION OF THE GINZBURG–LANDAU EQUATIONS FOR THE ABRIKOSOV VORTEX IN SUPERCONDUCTORS WITH AN ARBITRARY VALUE OF THE PARAMETER æ > 0.707

Until now, there is no exact analytical solution to the equations of the Ginzburg–Landau theory of superconductivity for any value of the parameter æ > 0.707, satisfying the boundary conditions for the Abrikosov vortex and the magnetic flux quantization condition, as well as the classical asymptotics (for the value æ >> 1) of the London and Abrikosov formulas. In this regard, the goal of this computational and analytical research was to find a satisfactorily accurate analytical solution to the equation of the Ginzburg–Landau theory for the Abrikosov vortex in superconductors with an arbitrary value æ > 0.707. By analytically solving the equations of the phenomenological theory of Ginzburg–Landau superconductivity for a single Abrikosov vortex in a massive type II superconductor with an arbitrary value of the parameter æ, we found: magnetic field strength h(ρ), current density j(ρ) and order parameter f(ρ), satisfying the boundary conditions, the quantization condition and the classical asymptotics of London and Abrikosov. The first critical magnetic field Hc1 and the ratio of absolute values Hc1/Hc2 in superconductors with æ > 0.707 are determined.