  In this paper, we apply the two-band extension [1] of BCS theory [2] into the
Mattis-Bardeen theory [3] to obtain the surface impedance of a two-band
superconductor, and apply it to magnesium diboride (MgB2) for radiofrequency
(RF) superconductivity applications. The numerical results for MgB2 are in good
agreement with the previously published experimental results [4]. The surface
impedance properties are clearly dominated by the smaller gap, significantly
limiting utility in the 10-20 K regime that might otherwise have been
attractive.
