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 λ, 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.