The upper critical field problem in MgB2

The upper critical field Hc2(T) for MgB2 is analyzed in terms of single and multi-band Eliashberg models. The relatively high value of Hc2(0) in the range of 14 to 18 Tesla can be understood, if a strongly coupled subgroup of heavy quasiparticles is involved in the superconductivity. The sizable coupling to both low- and high-frequency bosons is essential. This picture is supported by LDA calculations of Fermi velocity distribution over different sheets of the Fermi surface with special emphasis on the hole tubes. The possible origin of anharmonic soft modes is briefly discussed. Similarities and differences with transition metal borocarbides are figured out.