Upper critical field of a mixedd- ands-wave superconductor

Based on the linearized gap equation, the upper critical field ${(H}_{c2\mathrm{}})$ of a mixed $d$- and $s$-wave superconductor is microscopically obtained from the superconducting transition temperature ${(T}_c)$ down to zero temperature. It is shown that near $T_c,$ $H_{c2\mathrm{}}$ increases almost linearly with decreasing temperature. Moreover, the mixed $d$- and $s$-wave superconductor has a larger value of $H_{c2\mathrm{}}$ than that of a pure $d$-wave superconductor in the whole temperature region. Interestingly, our calculation unambiguously shows that $H_{c2\mathrm{}}$ finally becomes saturated. This implies that an admixture of the $s$-wave component could not be the origin of its upward curvature which has been reported in some experiments and some calculations based on the Ginzburg-Landau equations.