Why magnesium diboride is not described by anisotropic Ginzburg-Landau theory

It is well established that the superconductivity in the recently discovered superconducting compound MgB2 resides in the quasi-two-dimensional band (sigma band) and three-dimensional band (pi band). We demonstrate that, due to such band structure, the anisotropic Ginzburg-Landau theory practically does not have a region of applicability, because gradient expansion in the c direction breaks down. In the case of a dirty pi band, we derive the simplest equations, which describe properties of such superconductors near Tc, and explore some consequences of these equations.