Narrow Results

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 $\gamma$) and fourth (quartic, with coupling parameter $\tilde{\gamma }$) order between the two superconducting order parameters ($f_i$ with i = 1,2) 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 $f_i$-profiles, where our starting point was the calculation of the superconducting critical temperature $T_c$. With this at hand, we evaluate $f_i$ and the magnetic field along the z-axis, $B_0$, as function of $\gamma$, $\tilde{\gamma }$, the radial distance $r/{\lambda }_1(0)$ and the temperature $T$, for $T\approx T_c$. The self-consistent equations allow us to compute $\lambda$ (penetration depth) and the healing lengths of $f_i$ ($L_{h_i}$ with i = 1,2) as functions of T, $\gamma$ and $\tilde{\gamma }$. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.