Comparison of temperature and angular dependence of the upper critical field in Mg1-xAlxB2 single crystals in dirty-limit two-gap theory

We studied the temperature and the angular dependences of the upper critical field [H-c2(T,theta)] of Mg1-xAlxB2 single crystals (x=0.12 and 0.21) and compared with the dirty-limit two-gap theory. We found that H-c2(T,theta)'s were well described in a unified way by this theory. The values of the parameters obtained by fitting experimental data to the theory indicated that as the Al concentration was increased, anisotropic impurity scattering increased, making the sigma bands less anisotropic. Accordingly, the temperature dependence of the anisotropy ratio of H-c2 (gamma(H)) systematically decreased, and for x=0.21, gamma(H) was nearly independent of temperature. Our results imply that Mg1-xAlxB2 single crystals are in the dirty limit and that the two-gap nature survives until x=0.21.