Nonlinear microwave response of MgB2
  We calculate the intrinsic nonlinear microwave response of the two gap superconductor MgB2 in the clean and dirty limits. Due to the small value of the pi band gap, the nonlinear response at low temperatures is larger than for a single gap Bardeen-Cooper-Schrieffer (BCS) s-wave superconductor with a transition temperature of 40 K. Comparing this result with the intrinsic nonlinear d-wave response of YBa2Cu3O7 (YBCO) we find a comparable response at temperatures around 20 K. Due to its two gap nature, impurity scattering in MgB2 can be used to reduce the nonlinear response if the scattering rate in the pi band is made larger than the one in the sigma band. 
T. Dahm and D. J. Scalapino