Superconducting state in two band MgB2 simple ceramic

Many phenomena of current physical interest are directly related to the difference in the healing lengths of the band condensates, such as the non-monotonic interaction between vortices, being a possible explanation for highly debated unusual vortex configurations observed in a simple ceramic MgB2. Effects due to the difference in the spatial profiles of different band condensates can be accounted for within the full microscopic numerical treatment with an enormous computational effort. These difficulties have stimulated a search for a general Ginzburg-Landau formalism with a coexistence of two band condensates with different healing lengths. In this work, we derive the free-energy functional for the extended formalism and the corresponding expression for the current density; also, using the time dependent Ginzburg-Landau theory, we calculate the vortex state in a superconducting simple ceramic exposed to a homogeneous magnetic field.