Extended Ginzburg-Landau Formalism for Two-Band Superconductors

Recent observation of unusual vortex patterns in MgB2 single crystals raised speculations about possible type-1.5 superconductivity in two-band materials, mixing the properties of both type-I and type-II superconductors. However, the strict application of the standard two-band Ginzburg-Landau (GL) theory results in simply proportional order parameters of the two bands-and does not support the type-1.5 behavior. Here we derive the extended GL formalism (accounting all terms of the next order over the small tau = 1 - T/T-c parameter) for a two-band clean s-wave superconductor and show that the two condensates generally have different spatial scales, with the difference disappearing only in the limit T -> T-c. The extended version of the two-band GL formalism improves the validity of GL theory below T-c and suggests revisiting the earlier calculations based on the standard model.