Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

Abstract

A two-band and quartic interaction order Ginzburg–Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter [Formula: see text]) and fourth (quartic, with coupling parameter [Formula: see text]) order between the two superconducting order parameters ([Formula: see text] with i = 1,[Formula: see text]2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the [Formula: see text]-profiles, where our starting point was the calculation of the superconducting critical temperature [Formula: see text]. With this at hand, we evaluate [Formula: see text] and the magnetic field along the z-axis, [Formula: see text], as function of [Formula: see text], [Formula: see text], the radial distance [Formula: see text] and the temperature [Formula: see text], for [Formula: see text]. The self-consistent equations allow us to compute [Formula: see text] (penetration depth) and the healing lengths of [Formula: see text] ([Formula: see text] with i = 1,[Formula: see text]2) as functions of T, [Formula: see text] and [Formula: see text]. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.