London penetration depth λ(T) in two-band Ginzburg–Landau theory: application to MgB2

Two-band Ginzburg–Landau (G–L) theory equations were solved analytically to determine the temperature dependence of the London penetration depth λ(T). Its temperature dependence is non-linear near Tc. The strength of the non-linearity is mainly dependent on the interaction coupling between the order parameters of two separate bands. In addition, the inter-gradient interaction as well as the ratio of effective masses of two separate bands was also found to be important in determining its temperature dependence. The solutions were applied to MgB2, which was characterized as a two-band superconductor. The results of the calculations are in good agreement with the experimental data for bulk MgB2.