Interrelation of the critical magnetic field Hc2 and the residual resistivity for the two-band superconductor MgB2

An expression that describes the upper critical magnetic field Hc2 and generalizes the Gor’kov relation has been derived for the two-band two-gap superconductor MgB2. The expression relates the upper critical magnetic field Hc2 to the residual resistivity and the parameters of the band structure and holds in the range from the clean limit to the dirty limit. The ratios of the relaxation times τπ/τσ and the mean free paths of π- and σ-band electrons for MgB2 samples with a low defect level and Mg(B1 − xCx)2 samples with a partial substitution of carbon for boron are determined from experimental data.