It was well established that the superconductivity in the recently discovered superconducting compound MgB2 resides in the quasi 2-dimensional band (σ-band) and 3-dimensional band (π band). It was demonstrated  that, due to such band structure, the anisotropic Ginzburg-Landau theory practically did not have a region of applicability, because gradient expansion in the c-direction breaks down. In the case of a dirty π band, the simplest equations were derived which described the properties of such superconductors near to TC, and some consequences of these equations were explored.

Why Magnesium Diboride is not Described by Anisotropic Ginzburg-Landau Theory. A.E.Koshelev, A.A.Golubov: Physical Review Letters, 2004, 92[10], 107008 (3pp)