Ginzburg-Landau theory: the case of two-band superconductors

Recent studies of two-band superconductors using the Ginzburg-Landau (GL) theory are reviewed. The upper and lower critical fields [H-c2 (T) and H-c1 (T), respectively], thermodynamic magnetic field H-cm (T), critical current density j(c) (T), magnetization M(T) near the upper critical field, and the upper critical field H-c2(film)(T) of thin films are examined from the viewpoint of their temperature dependence at a point T-c using the two-band GL theory. The results are shown to be in good agreement with the experimental data for the bulky samples of superconducting magnesium diboride, MgB2, and nonmagnetic borocarbides LuNi2B2C and YNi2B2C. The specific heat jump turns out to be smaller than that calculated by single-band GL theory. The upper critical field of thin films of two-band superconductors is calculated and the Little-Parks effect is analyzed. It is shown that magnetic flux quantization and the relationship between the surface critical magnetic field H-c3(T) and the upper critical field H-c2(T) are the same as in the single-band GL theory. Extension of the two-band GL theory to the case of layered anisotropy is presented. The anisotropy parameter of the upper critical field H-c2 and the London penetration depth lambda, calculated for MgB2 single crystals, are in good agreement with the experimental data and show opposite temperature behavior to that in single-band GL theory.