The theory of multiband superconductivity was proposed soon after the original theory of BCS, but the first material to display properties predicted by the theory, magnesium diboride, was first observed in 2001.
Since then the number of materials showing these phenomena has grown, and these materials have attractive properties that warrant further investigation.
I will first discuss multiband BCS theory, and will look at a specific case of three bands. In this case there can be an additional phase transition to a new superconducting state, with characteristic discontinuities in the derivatives of the gap functions. I will discuss a procedure which both finds when this transition occurs, and simplifies the calculation of the value of the gaps in this case.
I will also outline the creation of an extended multiband Ginzburg-Landau theory. I show that this recreates the one-band result at first order, and can be applied in the one-band case over a very large temperature region with impressive performance. I will also show that in the two-band case the theory has mixed results, and outline a possible reason why the theory can break down.