Two-band Ginzburg-Landau theory for the lower critical field Hc1 in MgB2

The temperature dependence of the lower critical field H-cl(T) for the superconducting magnesium diboride. MgB2. is studied in the vicinity of T, using a two-band Ginzburg-Landau (G-L) theory. The theoretically calculated H-cl(T) near T-c exhibits a negative curvature. The results are shown to be in good agreement with the experimental data. In addition, two-band G-L theory calculations give a temperature dependence of the Ginzburg-Landau parameter kappa(T) = lambda(T)/xi(T), which varies little with the temperature in a manner similar to the microscopic single-band BSC theory.