We study the temperature dependence of the upper critical field Hc2(T) for superconducting magnesium diboride, MgB2 in the vicinity of Tc using a two-band Ginzburg-Landau (G-L) theory. The temperature dependence of Hc2(T) near Tc exhibits a positive curvature. In addition, the calculated temperature dependence and its higher-order derivatives are also shown to be in good agreement with the experimental data. In analogy with the multi-band character of the Eliashberg microscopic theory, the positive curvature of Hc2(T) is described reasonably by solving the two-band G-L theory.

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The temperature dependence of the lower critical field Hc1(T) for the superconducting magnesium diboride, MgB2, is studied in the vicinity of Tc using a two-band Ginzburg–Landau (G–L) theory. The theoretically calculated Hc1(T) near Tc 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 κ (T) = λ (T)/ξ (T), which varies little with the temperature in a manner similar to the microscopic single-band BSC theory.