Limits of the upper critical field in dirty two-gap superconductors

An overview of the theory of the upper critical field in dirty two-gap superconductors, with a particular emphasis on MgB2 is given. We focus here on the maximum Hc2 which may be achieved by increasing intraband scattering, and on the limitations imposed by weak interband scattering and paramagnetic effects. In particular, we discuss recent experiments which have demonstrated tenfold increase of Hc2 in dirty carbon-doped films as compared to single crystals, so that Hc2(0) parallel to the ab planes may approach the BCS paramagnetic limit, Hp [T] = 1.84Tc [K] ≃ 60–70 T. New effects produced by weak interband scattering in the two-gap Ginzburg–Landau equations and features of Hc2(T) in ultrathin MgB2 films are addressed.